LMFDB - Embedded newform 60.5.l.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(23,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	60.23
Dual form			60.5.l.a.47.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.98340 - 0.364047i) q^{2} +(-6.64241 - 6.07276i) q^{3} +(15.7349 + 2.90029i) q^{4} +(-22.0852 + 11.7150i) q^{5} +(24.2486 + 26.6084i) q^{6} +(-39.7479 - 39.7479i) q^{7} +(-61.6227 - 17.2813i) q^{8} +(7.24316 + 80.6755i) q^{9} +O(q^{10})$	\(q+(-3.98340 - 0.364047i) q^{2} +(-6.64241 - 6.07276i) q^{3} +(15.7349 + 2.90029i) q^{4} +(-22.0852 + 11.7150i) q^{5} +(24.2486 + 26.6084i) q^{6} +(-39.7479 - 39.7479i) q^{7} +(-61.6227 - 17.2813i) q^{8} +(7.24316 + 80.6755i) q^{9} +(92.2391 - 38.6257i) q^{10} +155.433 q^{11} +(-86.9051 - 114.819i) q^{12} +(115.123 + 115.123i) q^{13} +(143.862 + 172.802i) q^{14} +(217.842 + 56.3022i) q^{15} +(239.177 + 91.2717i) q^{16} +(151.054 + 151.054i) q^{17} +(0.517273 - 324.000i) q^{18} -121.587 q^{19} +(-381.487 + 120.282i) q^{20} +(22.6423 + 505.401i) q^{21} +(-619.153 - 56.5850i) q^{22} +(314.833 + 314.833i) q^{23} +(304.378 + 489.009i) q^{24} +(350.515 - 517.459i) q^{25} +(-416.670 - 500.490i) q^{26} +(441.811 - 579.866i) q^{27} +(-510.150 - 740.711i) q^{28} -203.047 q^{29} +(-847.254 - 303.579i) q^{30} +416.993i q^{31} +(-919.509 - 450.643i) q^{32} +(-1032.45 - 943.909i) q^{33} +(-546.717 - 656.698i) q^{34} +(1343.49 + 412.193i) q^{35} +(-120.012 + 1290.43i) q^{36} +(-1033.95 + 1033.95i) q^{37} +(484.328 + 44.2632i) q^{38} +(-65.5793 - 1463.80i) q^{39} +(1563.40 - 340.252i) q^{40} +2718.66i q^{41} +(93.7965 - 2021.46i) q^{42} +(205.575 - 205.575i) q^{43} +(2445.73 + 450.801i) q^{44} +(-1105.08 - 1696.88i) q^{45} +(-1139.49 - 1368.72i) q^{46} +(-2385.71 + 2385.71i) q^{47} +(-1034.44 - 2058.73i) q^{48} +758.791i q^{49} +(-1584.62 + 1933.64i) q^{50} +(-86.0473 - 1920.67i) q^{51} +(1477.56 + 2145.34i) q^{52} +(3371.95 - 3371.95i) q^{53} +(-1971.01 + 2149.00i) q^{54} +(-3432.78 + 1820.91i) q^{55} +(1762.48 + 3136.27i) q^{56} +(807.628 + 738.367i) q^{57} +(808.817 + 73.9186i) q^{58} -1035.14i q^{59} +(3264.44 + 1517.72i) q^{60} +4861.25 q^{61} +(151.805 - 1661.05i) q^{62} +(2918.78 - 3494.58i) q^{63} +(3498.72 + 2129.84i) q^{64} +(-3891.18 - 1193.84i) q^{65} +(3769.04 + 4135.83i) q^{66} +(4412.48 + 4412.48i) q^{67} +(1938.72 + 2814.92i) q^{68} +(-179.344 - 4003.16i) q^{69} +(-5201.60 - 2131.02i) q^{70} -3184.12 q^{71} +(947.831 - 5096.61i) q^{72} +(6718.28 + 6718.28i) q^{73} +(4495.05 - 3742.24i) q^{74} +(-5470.67 + 1308.58i) q^{75} +(-1913.16 - 352.636i) q^{76} +(-6178.15 - 6178.15i) q^{77} +(-271.665 + 5854.79i) q^{78} -4318.43 q^{79} +(-6351.53 + 786.209i) q^{80} +(-6456.07 + 1168.69i) q^{81} +(989.720 - 10829.5i) q^{82} +(-2967.39 - 2967.39i) q^{83} +(-1109.53 + 8018.13i) q^{84} +(-5105.66 - 1566.46i) q^{85} +(-893.725 + 744.047i) q^{86} +(1348.72 + 1233.06i) q^{87} +(-9578.22 - 2686.08i) q^{88} +10167.3 q^{89} +(3784.25 + 7161.67i) q^{90} -9151.77i q^{91} +(4040.77 + 5866.99i) q^{92} +(2532.30 - 2769.83i) q^{93} +(10371.7 - 8634.73i) q^{94} +(2685.27 - 1424.39i) q^{95} +(3371.10 + 8577.31i) q^{96} +(-1945.15 + 1945.15i) q^{97} +(276.236 - 3022.57i) q^{98} +(1125.83 + 12539.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^6	$ 88 q - 4 q^{6} + 148 q^{10} - 164 q^{12} - 8 q^{13} - 484 q^{16} + 456 q^{18} + 600 q^{21} - 348 q^{22} - 8 q^{25} - 148 q^{28} + 68 q^{30} - 328 q^{33} - 1556 q^{36} + 2232 q^{37} + 2024 q^{40} - 2116 q^{42} - 2504 q^{45} - 4432 q^{46} + 1540 q^{48} + 80 q^{52} + 3192 q^{57} - 1948 q^{58} + 2836 q^{60} - 7568 q^{61} + 3384 q^{66} + 8348 q^{70} + 5256 q^{72} + 5592 q^{73} - 256 q^{76} + 13176 q^{78} - 12648 q^{81} + 20400 q^{82} + 5816 q^{85} + 7932 q^{88} - 13152 q^{90} + 3680 q^{93} - 18028 q^{96} - 15208 q^{97}+O(q^{100}) $ 88 * q - 4 * q^6 + 148 * q^10 - 164 * q^12 - 8 * q^13 - 484 * q^16 + 456 * q^18 + 600 * q^21 - 348 * q^22 - 8 * q^25 - 148 * q^28 + 68 * q^30 - 328 * q^33 - 1556 * q^36 + 2232 * q^37 + 2024 * q^40 - 2116 * q^42 - 2504 * q^45 - 4432 * q^46 + 1540 * q^48 + 80 * q^52 + 3192 * q^57 - 1948 * q^58 + 2836 * q^60 - 7568 * q^61 + 3384 * q^66 + 8348 * q^70 + 5256 * q^72 + 5592 * q^73 - 256 * q^76 + 13176 * q^78 - 12648 * q^81 + 20400 * q^82 + 5816 * q^85 + 7932 * q^88 - 13152 * q^90 + 3680 * q^93 - 18028 * q^96 - 15208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.98340	−	0.364047i	−0.995850	−	0.0910117i
$2$	−3.98340	−	0.364047i	−0.995850	−	0.0910117i
$3$	−6.64241	−	6.07276i	−0.738045	−	0.674751i
$3$	−6.64241	−	6.07276i	−0.738045	−	0.674751i
$4$	15.7349	+	2.90029i	0.983434	+	0.181268i
$5$	−22.0852	+	11.7150i	−0.883409	+	0.468602i
$5$	−22.0852	+	11.7150i	−0.883409	+	0.468602i
$6$	24.2486	+	26.6084i	0.673572	+	0.739122i
$7$	−39.7479	−	39.7479i	−0.811182	−	0.811182i	0.173629	−	0.984811i	$-0.444451\pi$
$7$	−39.7479	−	39.7479i	−0.811182	−	0.811182i	−0.984811	+	0.173629i	$0.944451\pi$
$8$	−61.6227	−	17.2813i	−0.962855	−	0.270020i
$9$	7.24316	+	80.6755i	0.0894217	+	0.995994i
$10$	92.2391	−	38.6257i	0.922391	−	0.386257i
$11$	155.433			1.28457			0.642287	−	0.766465i	$-0.277986\pi$
$11$	155.433			1.28457			0.642287	+	0.766465i	$0.277986\pi$
$12$	−86.9051	−	114.819i	−0.603508	−	0.797357i
$13$	115.123	+	115.123i	0.681200	+	0.681200i	0.960270	−	0.279071i	$-0.0900265\pi$
$13$	115.123	+	115.123i	0.681200	+	0.681200i	−0.279071	+	0.960270i	$0.590026\pi$
$14$	143.862	+	172.802i	0.733988	+	0.881642i
$15$	217.842	+	56.3022i	0.968186	+	0.250232i
$16$	239.177	+	91.2717i	0.934284	+	0.356530i
$17$	151.054	+	151.054i	0.522677	+	0.522677i	0.918379	−	0.395702i	$-0.129499\pi$
$17$	151.054	+	151.054i	0.522677	+	0.522677i	−0.395702	+	0.918379i	$0.629499\pi$
$18$	0.517273	−	324.000i	0.00159652	−	0.999999i
$19$	−121.587			−0.336805			−0.168403	−	0.985718i	$-0.553861\pi$
$19$	−121.587			−0.336805			−0.168403	+	0.985718i	$0.553861\pi$
$20$	−381.487	+	120.282i	−0.953717	+	0.300705i
$21$	22.6423	+	505.401i	0.0513430	+	1.14603i
$22$	−619.153	−	56.5850i	−1.27924	−	0.116911i
$23$	314.833	+	314.833i	0.595148	+	0.595148i	0.939017	−	0.343870i	$-0.111738\pi$
$23$	314.833	+	314.833i	0.595148	+	0.595148i	−0.343870	+	0.939017i	$0.611738\pi$
$24$	304.378	+	489.009i	0.528434	+	0.848974i
$25$	350.515	−	517.459i	0.560824	−	0.827935i
$26$	−416.670	−	500.490i	−0.616375	−	0.740370i
$27$	441.811	−	579.866i	0.606051	−	0.795426i
$28$	−510.150	−	740.711i	−0.650702	−	0.944785i
$29$	−203.047			−0.241435			−0.120718	−	0.992687i	$-0.538520\pi$
$29$	−203.047			−0.241435			−0.120718	+	0.992687i	$0.538520\pi$
$30$	−847.254	−	303.579i	−0.941394	−	0.337310i
$31$			416.993i			0.433915i	0.976181	+	0.216958i	$0.0696134\pi$
$31$			416.993i			0.433915i	−0.976181	+	0.216958i	$0.930387\pi$
$32$	−919.509	−	450.643i	−0.897958	−	0.440081i
$33$	−1032.45	−	943.909i	−0.948073	−	0.866767i
$34$	−546.717	−	656.698i	−0.472938	−	0.568078i
$35$	1343.49	+	412.193i	1.09673	+	0.336484i
$36$	−120.012	+	1290.43i	−0.0926015	+	0.995703i
$37$	−1033.95	+	1033.95i	−0.755260	+	0.755260i	−0.975456	−	0.220195i	$-0.929331\pi$
$37$	−1033.95	+	1033.95i	−0.755260	+	0.755260i	0.220195	+	0.975456i	$0.429331\pi$
$38$	484.328	+	44.2632i	0.335407	+	0.0306532i
$39$	−65.5793	−	1463.80i	−0.0431159	−	0.962396i
$40$	1563.40	−	340.252i	0.977127	−	0.212658i
$41$			2718.66i			1.61729i	0.588299	+	0.808644i	$0.299798\pi$
$41$			2718.66i			1.61729i	−0.588299	+	0.808644i	$0.700202\pi$
$42$	93.7965	−	2021.46i	0.0531726	−	1.14595i
$43$	205.575	−	205.575i	0.111182	−	0.111182i	−0.649327	−	0.760509i	$-0.724950\pi$
$43$	205.575	−	205.575i	0.111182	−	0.111182i	0.760509	+	0.649327i	$0.224950\pi$
$44$	2445.73	+	450.801i	1.26329	+	0.232852i
$45$	−1105.08	−	1696.88i	−0.545721	−	0.837967i
$46$	−1139.49	−	1368.72i	−0.538512	−	0.646843i
$47$	−2385.71	+	2385.71i	−1.08000	+	1.08000i	−0.0834867	+	0.996509i	$0.526606\pi$
$47$	−2385.71	+	2385.71i	−1.08000	+	1.08000i	−0.996509	+	0.0834867i	$0.973394\pi$
$48$	−1034.44	−	2058.73i	−0.448975	−	0.893545i
$49$			758.791i			0.316031i
$50$	−1584.62	+	1933.64i	−0.633849	+	0.773457i
$51$	−86.0473	−	1920.67i	−0.0330824	−	0.738437i
$52$	1477.56	+	2145.34i	0.546435	+	0.793394i
$53$	3371.95	−	3371.95i	1.20041	−	1.20041i	0.226368	−	0.974042i	$-0.427315\pi$
$53$	3371.95	−	3371.95i	1.20041	−	1.20041i	0.974042	−	0.226368i	$-0.0726851\pi$
$54$	−1971.01	+	2149.00i	−0.675929	+	0.736967i
$55$	−3432.78	+	1820.91i	−1.13480	+	0.601953i
$56$	1762.48	+	3136.27i	0.562015	+	1.00009i
$57$	807.628	+	738.367i	0.248577	+	0.227260i
$58$	808.817	+	73.9186i	0.240433	+	0.0219734i
$59$		−	1035.14i		−	0.297368i	−0.988885	−	0.148684i	$-0.952496\pi$
$59$		−	1035.14i		−	0.297368i	0.988885	−	0.148684i	$-0.0475037\pi$
$60$	3264.44	+	1517.72i	0.906788	+	0.421588i
$61$	4861.25			1.30644			0.653218	−	0.757170i	$-0.273419\pi$
$61$	4861.25			1.30644			0.653218	+	0.757170i	$0.273419\pi$
$62$	151.805	−	1661.05i	0.0394914	−	0.432114i
$63$	2918.78	−	3494.58i	0.735395	−	0.880469i
$64$	3498.72	+	2129.84i	0.854179	+	0.519980i
$65$	−3891.18	−	1193.84i	−0.920990	−	0.282567i
$66$	3769.04	+	4135.83i	0.865252	+	0.949456i
$67$	4412.48	+	4412.48i	0.982954	+	0.982954i	0.999857	−	0.0169029i	$-0.00538062\pi$
$67$	4412.48	+	4412.48i	0.982954	+	0.982954i	−0.0169029	+	0.999857i	$0.505381\pi$
$68$	1938.72	+	2814.92i	0.419274	+	0.608763i
$69$	−179.344	−	4003.16i	−0.0376693	−	0.840822i
$70$	−5201.60	−	2131.02i	−1.06155	−	0.434903i
$71$	−3184.12			−0.631645			−0.315822	−	0.948818i	$-0.602280\pi$
$71$	−3184.12			−0.631645			−0.315822	+	0.948818i	$0.602280\pi$
$72$	947.831	−	5096.61i	0.182838	−	0.983143i
$73$	6718.28	+	6718.28i	1.26070	+	1.26070i	0.950753	+	0.309949i	$0.100312\pi$
$73$	6718.28	+	6718.28i	1.26070	+	1.26070i	0.309949	+	0.950753i	$0.399688\pi$
$74$	4495.05	−	3742.24i	0.820864	−	0.683388i
$75$	−5470.67	+	1308.58i	−0.972564	+	0.232636i
$76$	−1913.16	−	352.636i	−0.331225	−	0.0610520i
$77$	−6178.15	−	6178.15i	−1.04202	−	1.04202i
$78$	−271.665	+	5854.79i	−0.0446524	+	0.962326i
$79$	−4318.43			−0.691946			−0.345973	−	0.938244i	$-0.612451\pi$
$79$	−4318.43			−0.691946			−0.345973	+	0.938244i	$0.612451\pi$
$80$	−6351.53	+	786.209i	−0.992426	+	0.122845i
$81$	−6456.07	+	1168.69i	−0.984008	+	0.178127i
$82$	989.720	−	10829.5i	0.147192	−	1.61058i
$83$	−2967.39	−	2967.39i	−0.430743	−	0.430743i	0.458138	−	0.888881i	$-0.348516\pi$
$83$	−2967.39	−	2967.39i	−0.430743	−	0.430743i	−0.888881	+	0.458138i	$0.848516\pi$
$84$	−1109.53	+	8018.13i	−0.157247	+	1.13636i
$85$	−5105.66	−	1566.46i	−0.706666	−	0.216810i
$86$	−893.725	+	744.047i	−0.120839	+	0.100601i
$87$	1348.72	+	1233.06i	0.178190	+	0.162909i
$88$	−9578.22	−	2686.08i	−1.23686	−	0.346860i
$89$	10167.3			1.28358			0.641792	−	0.766879i	$-0.278191\pi$
$89$	10167.3			1.28358			0.641792	+	0.766879i	$0.278191\pi$
$90$	3784.25	+	7161.67i	0.467191	+	0.884156i
$91$		−	9151.77i		−	1.10515i
$92$	4040.77	+	5866.99i	0.477407	+	0.693169i
$93$	2532.30	−	2769.83i	0.292785	−	0.320249i
$94$	10371.7	−	8634.73i	1.17381	−	0.977221i
$95$	2685.27	−	1424.39i	0.297537	−	0.157828i
$96$	3371.10	+	8577.31i	0.365788	+	0.930698i
$97$	−1945.15	+	1945.15i	−0.206733	+	0.206733i	−0.802877	−	0.596144i	$-0.796699\pi$
$97$	−1945.15	+	1945.15i	−0.206733	+	0.206733i	0.596144	+	0.802877i	$0.296699\pi$
$98$	276.236	−	3022.57i	0.0287626	−	0.314720i
$99$	1125.83	+	12539.7i	0.114869	+	1.27943i
$100$	7016.12	−	7125.59i	0.701612	−	0.712559i
$101$			2400.00i			0.235271i	0.993057	+	0.117636i	$0.0375315\pi$
$101$			2400.00i			0.235271i	−0.993057	+	0.117636i	$0.962469\pi$
$102$	−356.454	+	7682.14i	−0.0342613	+	0.738383i
$103$	−10119.0	+	10119.0i	−0.953816	+	0.953816i	−0.998980	−	0.0451638i	$-0.985619\pi$
$103$	−10119.0	+	10119.0i	−0.953816	+	0.953816i	0.0451638	+	0.998980i	$0.485619\pi$
$104$	−5104.71	−	9083.64i	−0.471959	−	0.839834i
$105$	−6420.86	−	10896.6i	−0.582391	−	0.988358i
$106$	−14659.4	+	12204.3i	−1.30468	+	1.08618i
$107$	4517.57	−	4517.57i	0.394582	−	0.394582i	−0.481735	−	0.876317i	$-0.659993\pi$
$107$	4517.57	−	4517.57i	0.394582	−	0.394582i	0.876317	+	0.481735i	$0.159993\pi$
$108$	8633.65	−	7842.77i	0.740196	−	0.672391i
$109$		−	5893.48i		−	0.496043i	−0.968755	−	0.248021i	$-0.920220\pi$
$109$		−	5893.48i		−	0.496043i	0.968755	−	0.248021i	$-0.0797803\pi$
$110$	14337.0	−	6003.72i	1.18488	−	0.496175i
$111$	13146.9	−	588.987i	1.06703	−	0.0478035i
$112$	−5878.91	−	13134.6i	−0.468663	−	1.04708i
$113$	−7755.35	+	7755.35i	−0.607358	+	0.607358i	−0.942255	−	0.334897i	$-0.891299\pi$
$113$	−7755.35	+	7755.35i	−0.607358	+	0.607358i	0.334897	+	0.942255i	$0.391299\pi$
$114$	−2948.30	−	3235.22i	−0.226862	−	0.248940i
$115$	−10641.4	−	3264.88i	−0.804646	−	0.246872i
$116$	−3194.93	−	588.894i	−0.237435	−	0.0437645i
$117$	−8453.73	+	10121.4i	−0.617557	+	0.739385i
$118$	−376.839	+	4123.37i	−0.0270640	+	0.296134i
$119$		−	12008.1i		−	0.847973i
$120$	−12451.0	−	7234.08i	−0.864655	−	0.502366i
$121$	9518.53			0.650128
$122$	−19364.3	−	1769.72i	−1.30101	−	0.118901i
$123$	16509.8	−	18058.5i	1.09127	−	1.19363i
$124$	−1209.40	+	6561.35i	−0.0786550	+	0.426727i
$125$	−1679.15	+	15534.5i	−0.107466	+	0.994209i
$126$	−12898.9	+	12857.7i	−0.812476	+	0.809886i
$127$	16022.6	+	16022.6i	0.993400	+	0.993400i	0.999978	−	0.00657790i	$-0.00209383\pi$
$127$	16022.6	+	16022.6i	0.993400	+	0.993400i	−0.00657790	+	0.999978i	$0.502094\pi$
$128$	−13161.4	−	9757.68i	−0.803309	−	0.595562i
$129$	−2613.92	+	117.105i	−0.157077	+	0.00703714i
$130$	15065.5	+	6172.13i	0.891450	+	0.365215i
$131$	4912.57			0.286264			0.143132	−	0.989704i	$-0.454283\pi$
$131$	4912.57			0.286264			0.143132	+	0.989704i	$0.454283\pi$
$132$	−13508.0	−	17846.8i	−0.775250	−	1.02426i
$133$	4832.81	+	4832.81i	0.273210	+	0.273210i
$134$	−15970.3	−	19183.0i	−0.889414	−	1.06834i
$135$	−2964.35	+	17982.3i	−0.162653	+	0.986683i
$136$	−6697.94	−	11918.7i	−0.362129	−	0.644396i
$137$	7719.02	+	7719.02i	0.411265	+	0.411265i	0.882179	−	0.470914i	$-0.156076\pi$
$137$	7719.02	+	7719.02i	0.411265	+	0.411265i	−0.470914	+	0.882179i	$0.656076\pi$
$138$	−742.939	+	16011.5i	−0.0390117	+	0.840761i
$139$	5395.40			0.279250			0.139625	−	0.990204i	$-0.455410\pi$
$139$	5395.40			0.279250			0.139625	+	0.990204i	$0.455410\pi$
$140$	19944.3	+	10382.3i	1.01756	+	0.529711i
$141$	30334.7	−	1359.01i	1.52581	−	0.0683574i
$142$	12683.6	+	1159.17i	0.629023	+	0.0574871i
$143$	17893.9	+	17893.9i	0.875051	+	0.875051i
$144$	−5631.00	+	19956.8i	−0.271557	+	0.962422i
$145$	4484.34	−	2378.70i	0.213286	−	0.113137i
$146$	−24315.8	−	29207.4i	−1.14073	−	1.37021i
$147$	4607.96	−	5040.20i	0.213242	−	0.233245i
$148$	−19267.9	+	13270.4i	−0.879653	+	0.605844i
$149$	−248.567			−0.0111962			−0.00559810	−	0.999984i	$-0.501782\pi$
$149$	−248.567			−0.0111962			−0.00559810	+	0.999984i	$0.501782\pi$
$150$	22268.3	−	3221.02i	0.989700	−	0.143156i
$151$		−	7593.72i		−	0.333043i	−0.986038	−	0.166522i	$-0.946746\pi$
$151$		−	7593.72i		−	0.333043i	0.986038	−	0.166522i	$-0.0532535\pi$
$152$	7492.50	+	2101.17i	0.324294	+	0.0909440i
$153$	−11092.2	+	13280.4i	−0.473845	+	0.567322i
$154$	22360.9	+	26859.2i	0.942861	+	1.13253i
$155$	−4885.09	−	9209.38i	−0.203334	−	0.383325i
$156$	3213.57	−	23223.1i	0.132050	−	0.954269i
$157$	−19436.6	+	19436.6i	−0.788534	+	0.788534i	−0.981254	−	0.192720i	$-0.938269\pi$
$157$	−19436.6	+	19436.6i	−0.788534	+	0.788534i	0.192720	+	0.981254i	$0.438269\pi$
$158$	17202.1	+	1572.11i	0.689074	+	0.0629752i
$159$	−42874.9	+	1920.82i	−1.69593	+	0.0759789i
$160$	25586.9	−	819.531i	0.999487	−	0.0320129i
$161$		−	25027.9i		−	0.965546i
$162$	26142.6	−	2305.05i	0.996135	−	0.0878315i
$163$	29327.3	−	29327.3i	1.10382	−	1.10382i	0.109872	−	0.993946i	$-0.464956\pi$
$163$	29327.3	−	29327.3i	1.10382	−	1.10382i	0.993946	−	0.109872i	$-0.0350441\pi$
$164$	−7884.90	+	42778.0i	−0.293162	+	1.59050i
$165$	33859.9	+	8751.24i	1.24371	+	0.321441i
$166$	10740.0	+	12900.6i	0.389752	+	0.468158i
$167$	2169.15	−	2169.15i	0.0777781	−	0.0777781i	−0.667148	−	0.744926i	$-0.732485\pi$
$167$	2169.15	−	2169.15i	0.0777781	−	0.0777781i	0.744926	+	0.667148i	$0.232485\pi$
$168$	7338.69	−	31535.5i	0.260016	−	1.11733i
$169$		−	2054.52i		−	0.0719344i
$170$	19767.6	+	8098.52i	0.684001	+	0.280226i
$171$	−880.671	−	9809.06i	−0.0301177	−	0.335456i
$172$	3830.93	−	2638.48i	0.129493	−	0.0891860i
$173$	−5174.20	+	5174.20i	−0.172882	+	0.172882i	−0.788245	−	0.615362i	$-0.789010\pi$
$173$	−5174.20	+	5174.20i	−0.172882	+	0.172882i	0.615362	+	0.788245i	$0.289010\pi$
$174$	−4923.60	−	5402.75i	−0.162624	−	0.178450i
$175$	−34500.2	+	6635.67i	−1.12654	+	0.216675i
$176$	37176.0	+	14186.7i	1.20016	+	0.457989i
$177$	−6286.15	+	6875.81i	−0.200649	+	0.219471i
$178$	−40500.3	−	3701.36i	−1.27826	−	0.116821i
$179$			30526.9i			0.952745i	0.879244	+	0.476373i	$0.158049\pi$
$179$			30526.9i			0.952745i	−0.879244	+	0.476373i	$0.841951\pi$
$180$	−12467.0	−	29905.4i	−0.384783	−	0.923007i
$181$	−12101.4			−0.369383			−0.184691	−	0.982797i	$-0.559129\pi$
$181$	−12101.4			−0.369383			−0.184691	+	0.982797i	$0.559129\pi$
$182$	−3331.67	+	36455.2i	−0.100582	+	1.10057i
$183$	−32290.4	−	29521.2i	−0.964209	−	0.881519i
$184$	−13960.2	−	24841.6i	−0.412339	−	0.733742i
$185$	10722.3	−	34947.9i	0.313288	−	1.02112i
$186$	−11095.5	+	10111.5i	−0.320716	+	0.292273i
$187$	23478.8	+	23478.8i	0.671417	+	0.671417i
$188$	−44458.3	+	30619.8i	−1.25787	+	0.866335i
$189$	−40609.5	+	5487.38i	−1.13685	+	0.153618i
$190$	−11215.0	+	4696.36i	−0.310666	+	0.130093i
$191$	−49514.5			−1.35727			−0.678634	−	0.734476i	$-0.737428\pi$
$191$	−49514.5			−1.35727			−0.678634	+	0.734476i	$0.737428\pi$
$192$	−10305.9	−	35394.1i	−0.279566	−	0.960127i
$193$	−21053.2	−	21053.2i	−0.565202	−	0.565202i	0.365579	−	0.930780i	$-0.380871\pi$
$193$	−21053.2	−	21053.2i	−0.565202	−	0.565202i	−0.930780	+	0.365579i	$0.880871\pi$
$194$	8456.43	−	7040.18i	0.224690	−	0.187060i
$195$	18596.9	+	31560.2i	0.489070	+	0.829986i
$196$	−2200.71	+	11939.5i	−0.0572864	+	0.310796i
$197$	−1349.86	−	1349.86i	−0.0347820	−	0.0347820i	0.689502	−	0.724284i	$-0.257830\pi$
$197$	−1349.86	−	1349.86i	−0.0347820	−	0.0347820i	−0.724284	+	0.689502i	$0.757830\pi$
$198$	80.4015	−	50360.3i	0.00205085	−	1.28457i
$199$	17439.6			0.440383			0.220192	−	0.975457i	$-0.429332\pi$
$199$	17439.6			0.440383			0.220192	+	0.975457i	$0.429332\pi$
$200$	−30542.0	+	25829.9i	−0.763551	+	0.645747i
$201$	−2513.56	−	56105.4i	−0.0622152	−	1.38871i
$202$	873.713	−	9560.17i	0.0214124	−	0.234295i
$203$	8070.69	+	8070.69i	0.195848	+	0.195848i
$204$	4216.56	−	30471.2i	0.101321	−	0.732200i
$205$	−31849.2	−	60042.3i	−0.757864	−	1.42873i
$206$	43991.9	−	36624.3i	1.03667	−	0.863049i
$207$	−23118.9	+	27679.7i	−0.539544	+	0.645983i
$208$	17027.2	+	38042.1i	0.393566	+	0.879302i
$209$	−18898.6			−0.432651
$210$	21610.0	+	45743.2i	0.490022	+	1.03726i
$211$		−	71584.0i		−	1.60787i	−0.594717	−	0.803935i	$-0.702736\pi$
$211$		−	71584.0i		−	1.60787i	0.594717	−	0.803935i	$-0.297264\pi$
$212$	62837.1	−	43277.8i	1.39812	−	0.962927i
$213$	21150.2	+	19336.4i	0.466182	+	0.426203i
$214$	−19639.9	+	16350.7i	−0.428856	+	0.357033i
$215$	−2131.85	+	6948.48i	−0.0461189	+	0.150319i
$216$	−37246.4	+	28097.8i	−0.798320	+	0.602234i
$217$	16574.6	−	16574.6i	0.351984	−	0.351984i
$218$	−2145.50	+	23476.1i	−0.0451457	+	0.493984i
$219$	−3827.05	−	85424.1i	−0.0797950	−	1.78112i
$220$	−59295.8	+	18695.8i	−1.22512	+	0.386278i
$221$			34779.4i			0.712095i
$222$	−52583.6	−	2439.90i	−1.06695	−	0.0495070i
$223$	−53356.9	+	53356.9i	−1.07295	+	1.07295i	−0.0758318	+	0.997121i	$0.524161\pi$
$223$	−53356.9	+	53356.9i	−1.07295	+	1.07295i	−0.997121	+	0.0758318i	$0.975839\pi$
$224$	18636.4	+	54460.7i	0.371421	+	1.08539i
$225$	44285.1	+	24530.0i	0.874768	+	0.484542i
$226$	33716.0	−	28069.4i	0.660114	−	0.549561i
$227$	−26624.0	+	26624.0i	−0.516680	+	0.516680i	−0.916565	−	0.399885i	$-0.869050\pi$
$227$	−26624.0	+	26624.0i	−0.516680	+	0.516680i	0.399885	+	0.916565i	$0.369050\pi$
$228$	10566.5	+	13960.5i	0.203265	+	0.268554i
$229$		−	40812.9i		−	0.778263i	−0.921182	−	0.389131i	$-0.872775\pi$
$229$		−	40812.9i		−	0.778263i	0.921182	−	0.389131i	$-0.127225\pi$
$230$	41200.6	+	16879.3i	0.778839	+	0.319079i
$231$	3519.36	+	78556.2i	0.0659539	+	1.47217i
$232$	12512.3	+	3508.91i	0.232467	+	0.0651922i
$233$	41404.1	−	41404.1i	0.762661	−	0.762661i	−0.214141	−	0.976803i	$-0.568695\pi$
$233$	41404.1	−	41404.1i	0.762661	−	0.762661i	0.976803	+	0.214141i	$0.0686953\pi$
$234$	37359.3	−	37240.2i	0.682286	−	0.680111i
$235$	24740.3	−	80637.7i	0.447990	−	1.46017i
$236$	3002.20	−	16287.8i	0.0539033	−	0.292442i
$237$	28684.8	+	26224.8i	0.510687	+	0.466891i
$238$	−4371.53	+	47833.2i	−0.0771754	+	0.844453i
$239$			14372.8i			0.251621i	0.992054	+	0.125810i	$0.0401531\pi$
$239$			14372.8i			0.251621i	−0.992054	+	0.125810i	$0.959847\pi$
$240$	46963.9	+	33349.0i	0.815345	+	0.578975i
$241$	−7842.45			−0.135026			−0.0675130	−	0.997718i	$-0.521506\pi$
$241$	−7842.45			−0.135026			−0.0675130	+	0.997718i	$0.521506\pi$
$242$	−37916.1	−	3465.19i	−0.647430	−	0.0591693i
$243$	49981.1	+	31443.3i	0.846433	+	0.532494i
$244$	76491.4	+	14099.0i	1.28479	+	0.236815i
$245$	−8889.28	−	16758.1i	−0.148093	−	0.279185i
$246$	−72339.1	+	65923.7i	−1.19537	+	1.08936i
$247$	−13997.4	−	13997.4i	−0.229431	−	0.229431i
$248$	7206.16	−	25696.2i	0.117166	−	0.417797i
$249$	1690.36	+	37730.8i	0.0272635	+	0.608552i
$250$	12344.0	−	61268.9i	0.197504	−	0.980302i
$251$	−15002.7			−0.238134			−0.119067	−	0.992886i	$-0.537990\pi$
$251$	−15002.7			−0.238134			−0.119067	+	0.992886i	$0.537990\pi$
$252$	56062.1	−	46521.7i	0.882813	−	0.732580i
$253$	48935.6	+	48935.6i	0.764511	+	0.764511i
$254$	−57991.3	−	69657.2i	−0.898867	−	1.07969i
$255$	24401.2	+	41410.5i	0.375258	+	0.636839i
$256$	48874.9	+	43660.1i	0.745773	+	0.666201i
$257$	7461.72	+	7461.72i	0.112972	+	0.112972i	0.761333	−	0.648361i	$-0.224545\pi$
$257$	7461.72	+	7461.72i	0.112972	+	0.112972i	−0.648361	+	0.761333i	$0.724545\pi$
$258$	10454.9	+	485.112i	0.157065	+	0.00728790i
$259$	82194.8			1.22531
$260$	−57765.0	−	30070.6i	−0.854512	−	0.444832i
$261$	−1470.70	−	16380.9i	−0.0215895	−	0.240468i
$262$	−19568.7	−	1788.41i	−0.285076	−	0.0260534i
$263$	−16600.0	−	16600.0i	−0.239992	−	0.239992i	0.576855	−	0.816847i	$-0.304280\pi$
$263$	−16600.0	−	16600.0i	−0.239992	−	0.239992i	−0.816847	+	0.576855i	$0.804280\pi$
$264$	47310.5	+	76008.3i	0.678813	+	1.09057i
$265$	−34967.8	+	113973.i	−0.497939	+	1.62297i
$266$	−17491.7	−	21010.4i	−0.247211	−	0.296942i
$267$	−67535.2	−	61743.4i	−0.947343	−	0.866100i
$268$	56632.7	+	82227.6i	0.788492	+	1.14485i
$269$	−18957.4			−0.261984			−0.130992	−	0.991383i	$-0.541816\pi$
$269$	−18957.4			−0.261984			−0.130992	+	0.991383i	$0.541816\pi$
$270$	18354.6	−	70551.5i	0.251777	−	0.967785i
$271$			43371.5i			0.590562i	0.955410	+	0.295281i	$0.0954133\pi$
$271$			43371.5i			0.590562i	−0.955410	+	0.295281i	$0.904587\pi$
$272$	22341.6	+	49915.5i	0.301979	+	0.674679i
$273$	−55576.5	+	60789.8i	−0.745703	+	0.815653i
$274$	−27937.9	−	33558.0i	−0.372128	−	0.446988i
$275$	54481.8	−	80430.4i	0.720420	−	1.06354i
$276$	8788.34	−	63509.6i	0.115369	−	0.833721i
$277$	−7063.88	+	7063.88i	−0.0920627	+	0.0920627i	−0.751638	−	0.659576i	$-0.770736\pi$
$277$	−7063.88	+	7063.88i	−0.0920627	+	0.0920627i	0.659576	+	0.751638i	$0.270736\pi$
$278$	−21492.0	−	1964.18i	−0.278091	−	0.0254151i
$279$	−33641.1	+	3020.34i	−0.432177	+	0.0388014i
$280$	−75666.3	−	48617.7i	−0.965131	−	0.620123i
$281$			151591.i			1.91982i	0.280305	+	0.959911i	$0.409564\pi$
$281$			151591.i			1.91982i	−0.280305	+	0.959911i	$0.590436\pi$
$282$	−121330.	−	5629.76i	−1.52570	−	0.0707933i
$283$	−7077.18	+	7077.18i	−0.0883665	+	0.0883665i	−0.749908	−	0.661542i	$-0.769902\pi$
$283$	−7077.18	+	7077.18i	−0.0883665	+	0.0883665i	0.661542	+	0.749908i	$0.269902\pi$
$284$	−50101.9	−	9234.87i	−0.621181	−	0.114497i
$285$	−26486.7	−	6845.60i	−0.326090	−	0.0842794i
$286$	−64764.4	−	77792.8i	−0.791779	−	0.951059i
$287$	108061.	−	108061.i	1.31191	−	1.31191i
$288$	29695.7	−	77445.9i	0.358021	−	0.933713i
$289$		−	37886.5i		−	0.453617i
$290$	−18728.9	+	7842.82i	−0.222698	+	0.0932559i
$291$	24732.9	−	1108.05i	0.292071	−	0.0130850i
$292$	86226.8	+	125197.i	1.01129	+	1.46834i
$293$	24386.0	−	24386.0i	0.284057	−	0.284057i	−0.550668	−	0.834725i	$-0.685627\pi$
$293$	24386.0	−	24386.0i	0.284057	−	0.284057i	0.834725	+	0.550668i	$0.185627\pi$
$294$	−20190.2	+	18399.6i	−0.233586	+	0.212870i
$295$	12126.7	+	22861.3i	0.139347	+	0.262698i
$296$	81582.9	−	45846.9i	0.931141	−	0.523271i
$297$	68672.2	−	90130.4i	0.778516	−	1.02178i
$298$	990.141	+	90.4900i	0.0111497	+	0.00101899i
$299$			72488.9i			0.810829i
$300$	−89875.9	+	4723.91i	−0.998622	+	0.0524878i
$301$	−16342.3			−0.180377
$302$	−2764.47	+	30248.8i	−0.0303108	+	0.331661i
$303$	14574.6	−	15941.8i	0.158750	−	0.173641i
$304$	−29080.7	−	11097.4i	−0.314672	−	0.120081i
$305$	−107362.	+	56949.7i	−1.15412	+	0.612198i
$306$	49019.5	−	48863.2i	0.523511	−	0.521842i
$307$	10740.0	+	10740.0i	0.113954	+	0.113954i	0.761784	−	0.647831i	$-0.224324\pi$
$307$	10740.0	+	10740.0i	0.113954	+	0.113954i	−0.647831	+	0.761784i	$0.724324\pi$
$308$	−79294.4	−	115131.i	−0.835874	−	1.21364i
$309$	128665.	−	5764.28i	1.34755	−	0.0603709i
$310$	16106.6	+	38463.0i	0.167603	+	0.400240i
$311$	151272.			1.56400			0.782001	−	0.623277i	$-0.214199\pi$
$311$	151272.			1.56400			0.782001	+	0.623277i	$0.214199\pi$
$312$	−21255.2	+	91336.9i	−0.218352	+	0.938290i
$313$	−104536.	−	104536.i	−1.06704	−	1.06704i	−0.997585	−	0.0694500i	$-0.977876\pi$
$313$	−104536.	−	104536.i	−1.06704	−	1.06704i	−0.0694500	−	0.997585i	$-0.522124\pi$
$314$	84499.4	−	70347.8i	0.857027	−	0.713495i
$315$	−23522.8	+	111372.i	−0.237065	+	1.12242i
$316$	−67950.3	−	12524.7i	−0.680483	−	0.125428i
$317$	−82778.0	−	82778.0i	−0.823752	−	0.823752i	0.162892	−	0.986644i	$-0.447918\pi$
$317$	−82778.0	−	82778.0i	−0.823752	−	0.823752i	−0.986644	+	0.162892i	$0.947918\pi$
$318$	171487.	+	7957.08i	1.69581	+	0.0786864i
$319$	−31560.3			−0.310141
$320$	−102221.	−	6050.30i	−0.998253	−	0.0590850i
$321$	−57441.7	+	2573.42i	−0.557464	+	0.0249747i
$322$	−9111.33	+	99696.2i	−0.0878760	+	0.961538i
$323$	−18366.1	−	18366.1i	−0.176040	−	0.176040i
$324$	−104975.	−	335.193i	−0.999995	−	0.00319304i
$325$	99923.6	−	19219.0i	0.946022	−	0.181955i
$326$	−127499.	+	106146.i	−1.19970	+	0.998776i
$327$	−35789.7	+	39146.9i	−0.334705	+	0.366102i
$328$	46981.9	−	167531.i	0.436700	−	1.55721i
$329$	189654.			1.75215
$330$	−131692.	−	47186.3i	−1.20929	−	0.433299i
$331$			78953.6i			0.720636i	0.932830	+	0.360318i	$0.117332\pi$
$331$			78953.6i			0.720636i	−0.932830	+	0.360318i	$0.882668\pi$
$332$	−38085.4	−	55297.9i	−0.345527	−	0.501687i
$333$	−90903.6	−	75925.5i	−0.819771	−	0.684698i
$334$	−9430.28	+	7850.93i	−0.0845340	+	0.0703766i
$335$	−149143.	−	45758.3i	−1.32897	−	0.407737i
$336$	−40713.3	+	122947.i	−0.360627	+	1.08903i
$337$	77935.2	−	77935.2i	0.686236	−	0.686236i	−0.275162	−	0.961398i	$-0.588731\pi$
$337$	77935.2	−	77935.2i	0.686236	−	0.686236i	0.961398	+	0.275162i	$0.0887314\pi$
$338$	−747.940	+	8183.96i	−0.00654687	+	0.0716358i
$339$	98610.6	−	4417.82i	0.858073	−	0.0384422i
$340$	−75794.1	−	39456.0i	−0.655658	−	0.341315i
$341$			64814.6i			0.557396i
$342$	−62.8935	+	39394.0i	−0.000537717	+	0.336805i
$343$	−65274.4	+	65274.4i	−0.554823	+	0.554823i
$344$	−16220.7	+	9115.48i	−0.137073	+	0.0770305i
$345$	50858.0	+	86309.6i	0.427289	+	0.725139i
$346$	22494.6	−	18727.3i	0.187899	−	0.156431i
$347$	22554.3	−	22554.3i	0.187314	−	0.187314i	−0.607220	−	0.794534i	$-0.707715\pi$
$347$	22554.3	−	22554.3i	0.187314	−	0.187314i	0.794534	+	0.607220i	$0.207715\pi$
$348$	17645.8	+	23313.7i	0.145708	+	0.192510i
$349$			188311.i			1.54606i	0.634371	+	0.773029i	$0.281259\pi$
$349$			188311.i			1.54606i	−0.634371	+	0.773029i	$0.718741\pi$
$350$	139844.	−	13872.9i	1.14158	−	0.113248i
$351$	117618.	−	15893.2i	0.954685	−	0.129002i
$352$	−142922.	−	70045.0i	−1.15349	−	0.565317i
$353$	119716.	−	119716.i	0.960734	−	0.960734i	−0.0385238	−	0.999258i	$-0.512266\pi$
$353$	119716.	−	119716.i	0.960734	−	0.960734i	0.999258	+	0.0385238i	$0.0122655\pi$
$354$	27543.3	−	25100.6i	0.219791	−	0.200299i
$355$	70322.0	−	37302.1i	0.558001	−	0.295990i
$356$	159981.	+	29488.0i	1.26232	+	0.232673i
$357$	−72922.6	+	79763.0i	−0.572170	+	0.625842i
$358$	11113.2	−	121601.i	0.0867110	−	0.948791i
$359$			32038.3i			0.248588i	0.992245	+	0.124294i	$0.0396666\pi$
$359$			32038.3i			0.248588i	−0.992245	+	0.124294i	$0.960333\pi$
$360$	38774.0	+	123664.i	0.299182	+	0.954196i
$361$	−115538.			−0.886562
$362$	48204.5	+	4405.46i	0.367850	+	0.0336182i
$363$	−63225.9	−	57803.7i	−0.479824	−	0.438675i
$364$	26542.8	−	144003.i	0.200329	−	1.08684i
$365$	−227080.	−	69669.8i	−1.70448	−	0.522949i
$366$	117878.	+	129350.i	0.879978	+	0.965615i
$367$	−134894.	−	134894.i	−1.00152	−	1.00152i	−0.999999	−	0.00152075i	$-0.999516\pi$
$367$	−134894.	−	134894.i	−1.00152	−	1.00152i	−0.00152075	−	0.999999i	$-0.500484\pi$
$368$	46565.4	+	104036.i	0.343849	+	0.768225i
$369$	−219329.	+	19691.7i	−1.61081	+	0.144621i
$370$	−55433.7	+	135308.i	−0.404921	+	0.988370i
$371$	−268056.			−1.94750
$372$	47878.9	−	36238.8i	0.345985	−	0.261871i
$373$	53176.5	+	53176.5i	0.382210	+	0.382210i	0.871898	−	0.489688i	$-0.162889\pi$
$373$	53176.5	+	53176.5i	0.382210	+	0.382210i	−0.489688	+	0.871898i	$0.662889\pi$
$374$	−84978.0	−	102073.i	−0.607524	−	0.729738i
$375$	105491.	−	92989.5i	0.750158	−	0.661259i
$376$	188242.	−	105786.i	1.33150	−	0.748259i
$377$	−23375.3	−	23375.3i	−0.164465	−	0.164465i
$378$	163762.	−	7074.66i	1.14612	−	0.0495133i
$379$	−113372.			−0.789271			−0.394635	−	0.918838i	$-0.629129\pi$
$379$	−113372.			−0.789271			−0.394635	+	0.918838i	$0.629129\pi$
$380$	46383.7	−	14624.7i	0.321217	−	0.101279i
$381$	−9127.20	−	203729.i	−0.0628764	−	1.40347i
$382$	197236.	+	18025.6i	1.35164	+	0.123527i
$383$	44520.9	+	44520.9i	0.303505	+	0.303505i	0.842384	−	0.538878i	$-0.181152\pi$
$383$	44520.9	+	44520.9i	0.303505	+	0.303505i	−0.538878	+	0.842384i	$0.681152\pi$
$384$	28167.5	+	144741.i	0.191023	+	0.981586i
$385$	208823.	+	64068.6i	1.40883	+	0.432239i
$386$	76199.0	+	91527.7i	0.511416	+	0.614296i
$387$	18073.8	+	15095.8i	0.120678	+	0.100794i
$388$	−36248.3	+	24965.3i	−0.240782	+	0.165834i
$389$	80942.5			0.534906			0.267453	−	0.963571i	$-0.413818\pi$
$389$	80942.5			0.534906			0.267453	+	0.963571i	$0.413818\pi$
$390$	−62589.4	−	132487.i	−0.411502	−	0.871052i
$391$			95113.4i			0.622140i
$392$	13112.9	−	46758.8i	0.0853347	−	0.304292i
$393$	−32631.3	−	29832.9i	−0.211276	−	0.193157i
$394$	4885.61	+	5868.43i	0.0314721	+	0.0378033i
$395$	95373.7	−	50590.7i	0.611272	−	0.324247i
$396$	−18653.8	+	200576.i	−0.118953	+	1.27905i
$397$	79054.7	−	79054.7i	0.501587	−	0.501587i	−0.410344	−	0.911931i	$-0.634591\pi$
$397$	79054.7	−	79054.7i	0.501587	−	0.501587i	0.911931	+	0.410344i	$0.134591\pi$
$398$	−69469.0	−	6348.84i	−0.438556	−	0.0400800i
$399$	−2753.00	−	61450.0i	−0.0172926	−	0.385990i
$400$	131064.	−	91772.0i	0.819153	−	0.573575i
$401$			16370.9i			0.101809i	0.998704	+	0.0509043i	$0.0162104\pi$
$401$			16370.9i			0.101809i	−0.998704	+	0.0509043i	$0.983790\pi$
$402$	−10412.5	+	224405.i	−0.0644323	+	1.38861i
$403$	−48005.3	+	48005.3i	−0.295583	+	0.295583i
$404$	−6960.70	+	37763.9i	−0.0426472	+	0.231374i
$405$	128893.	−	101444.i	0.785811	−	0.618467i
$406$	−29210.7	−	35086.9i	−0.177210	−	0.212859i
$407$	−160711.	+	160711.i	−0.970187	+	0.970187i
$408$	−27889.2	+	119844.i	−0.167539	+	0.719940i
$409$			250150.i			1.49539i	0.664045	+	0.747693i	$0.268838\pi$
$409$			250150.i			1.49539i	−0.664045	+	0.747693i	$0.731162\pi$
$410$	105010.	+	250767.i	0.624688	+	1.49177i
$411$	−4397.12	−	98148.7i	−0.0260306	−	0.581033i
$412$	−188570.	+	129874.i	−1.11091	+	0.765118i
$413$	−41144.6	+	41144.6i	−0.241219	+	0.241219i
$414$	102169.	−	101843.i	0.596097	−	0.594197i
$415$	100299.	+	30772.4i	0.582369	+	0.178675i
$416$	−53977.1	−	157736.i	−0.311905	−	0.911472i
$417$	−35838.4	−	32765.0i	−0.206099	−	0.188425i
$418$	75280.7	+	6879.98i	0.430855	+	0.0393763i
$419$			42304.8i			0.240969i	0.992715	+	0.120485i	$0.0384449\pi$
$419$			42304.8i			0.240969i	−0.992715	+	0.120485i	$0.961555\pi$
$420$	−69428.4	−	190080.i	−0.393585	−	1.07755i
$421$	197524.			1.11444			0.557219	−	0.830365i	$-0.311868\pi$
$421$	197524.			1.11444			0.557219	+	0.830365i	$0.311868\pi$
$422$	−26059.9	+	285148.i	−0.146335	+	1.60120i
$423$	−209748.	−	175188.i	−1.17224	−	0.979094i
$424$	−266060.	+	149517.i	−1.47995	+	0.831686i
$425$	131111.	−	25217.5i	0.725873	−	0.139613i
$426$	−77210.4	−	84724.3i	−0.425458	−	0.466862i
$427$	−193224.	−	193224.i	−1.05976	−	1.05976i
$428$	84186.0	−	57981.5i	0.459571	−	0.316520i
$429$	−10193.2	−	227524.i	−0.0553856	−	1.23627i
$430$	11021.6	−	26902.5i	0.0596083	−	0.145497i
$431$	−239676.			−1.29024			−0.645120	−	0.764081i	$-0.723193\pi$
$431$	−239676.			−1.29024			−0.645120	+	0.764081i	$0.723193\pi$
$432$	158596.	−	98365.5i	0.849817	−	0.527078i
$433$	2249.70	+	2249.70i	0.0119991	+	0.0119991i	0.713081	−	0.701082i	$-0.247299\pi$
$433$	2249.70	+	2249.70i	0.0119991	+	0.0119991i	−0.701082	+	0.713081i	$0.747299\pi$
$434$	−72057.1	+	59989.3i	−0.382558	+	0.318489i
$435$	−44232.1	−	11432.0i	−0.233754	−	0.0604148i
$436$	17092.8	−	92733.6i	0.0899166	−	0.487825i
$437$	−38279.5	−	38279.5i	−0.200449	−	0.200449i
$438$	−15853.7	+	341671.i	−0.0826385	+	1.78099i
$439$	261743.			1.35814			0.679072	−	0.734072i	$-0.262382\pi$
$439$	261743.			1.35814			0.679072	+	0.734072i	$0.262382\pi$
$440$	243005.	−	52886.6i	1.25519	−	0.273174i
$441$	−61215.9	+	5496.04i	−0.314765	+	0.0282601i
$442$	12661.3	−	138540.i	0.0648090	−	0.709140i
$443$	197290.	+	197290.i	1.00530	+	1.00530i	0.999986	+	0.00531685i	$0.00169241\pi$
$443$	197290.	+	197290.i	1.00530	+	1.00530i	0.00531685	+	0.999986i	$0.498308\pi$
$444$	208573.	+	28862.0i	1.05802	+	0.146407i
$445$	−224547.	+	119110.i	−1.13393	+	0.601490i
$446$	231966.	−	193117.i	1.16615	−	0.970848i
$447$	1651.08	+	1509.49i	0.00826330	+	0.00755465i
$448$	−54410.1	−	223723.i	−0.271096	−	1.11469i
$449$	465.936			0.00231118			0.00115559	−	0.999999i	$-0.499632\pi$
$449$	465.936			0.00231118			0.00115559	+	0.999999i	$0.499632\pi$
$450$	−167475.	−	113834.i	−0.827038	−	0.562145i
$451$			422570.i			2.07752i
$452$	−144523.	+	99537.3i	−0.707391	+	0.487202i
$453$	−46114.8	+	50440.6i	−0.224721	+	0.245801i
$454$	115746.	−	96361.6i	0.561560	−	0.467512i
$455$	107213.	+	202119.i	0.517877	+	0.976303i
$456$	−37008.3	−	59457.0i	−0.177979	−	0.285939i
$457$	114079.	−	114079.i	0.546225	−	0.546225i	−0.379122	−	0.925347i	$-0.623774\pi$
$457$	114079.	−	114079.i	0.546225	−	0.546225i	0.925347	+	0.379122i	$0.123774\pi$
$458$	−14857.8	+	162574.i	−0.0708310	+	0.775033i
$459$	154328.	−	20853.7i	0.732520	−	0.0989821i
$460$	−157973.	−	82235.9i	−0.746566	−	0.388639i
$461$			30776.4i			0.144816i	0.997375	+	0.0724079i	$0.0230683\pi$
$461$			30776.4i			0.144816i	−0.997375	+	0.0724079i	$0.976932\pi$
$462$	14579.1	−	314202.i	0.0683041	−	1.47206i
$463$	103074.	−	103074.i	0.480825	−	0.480825i	−0.424570	−	0.905395i	$-0.639575\pi$
$463$	103074.	−	103074.i	0.480825	−	0.480825i	0.905395	+	0.424570i	$0.139575\pi$
$464$	−48564.1	−	18532.4i	−0.225569	−	0.0860789i
$465$	−23477.6	+	90838.4i	−0.108580	+	0.420111i
$466$	−180002.	+	149856.i	−0.828907	+	0.690085i
$467$	185501.	−	185501.i	0.850576	−	0.850576i	−0.139628	−	0.990204i	$-0.544591\pi$
$467$	185501.	−	185501.i	0.850576	−	0.850576i	0.990204	+	0.139628i	$0.0445908\pi$
$468$	−162374.	+	134742.i	−0.741353	+	0.615193i
$469$		−	350774.i		−	1.59471i
$470$	−127906.	+	312205.i	−0.579023	+	1.41333i
$471$	247139.	−	11072.0i	1.11404	−	0.0499096i
$472$	−17888.5	+	63788.0i	−0.0802952	+	0.286322i
$473$	31953.2	−	31953.2i	0.142821	−	0.142821i
$474$	−104716.	−	114907.i	−0.466075	−	0.511432i
$475$	−42618.0	+	62916.1i	−0.188889	+	0.278853i
$476$	34827.1	−	188947.i	0.153710	−	0.833925i
$477$	296457.	+	247610.i	1.30294	+	1.08826i
$478$	5232.39	−	57252.8i	0.0229005	−	0.250577i
$479$		−	162482.i		−	0.708166i	−0.935214	−	0.354083i	$-0.884793\pi$
$479$		−	162482.i		−	0.708166i	0.935214	−	0.354083i	$-0.115207\pi$
$480$	−174935.	−	149939.i	−0.759268	−	0.650778i
$481$	−238063.			−1.02897
$482$	31239.6	+	2855.02i	0.134466	+	0.0122890i
$483$	−151989.	+	166246.i	−0.651503	+	0.712616i
$484$	149773.	+	27606.5i	0.639358	+	0.117847i
$485$	20171.6	−	65746.6i	0.0857543	−	0.279505i
$486$	−187648.	−	143447.i	−0.794457	−	0.607320i
$487$	105392.	+	105392.i	0.444377	+	0.444377i	0.893480	−	0.449103i	$-0.148256\pi$
$487$	105392.	+	105392.i	0.444377	+	0.444377i	−0.449103	+	0.893480i	$0.648256\pi$
$488$	−299563.	−	84008.5i	−1.25791	−	0.352763i
$489$	−372902.	+	16706.2i	−1.55947	+	0.0698652i
$490$	29308.8	+	69990.2i	0.122069	+	0.291505i
$491$	53907.5			0.223608			0.111804	−	0.993730i	$-0.464337\pi$
$491$	53907.5			0.223608			0.111804	+	0.993730i	$0.464337\pi$
$492$	312155.	−	236266.i	1.28956	−	0.976046i
$493$	−30671.0	−	30671.0i	−0.126193	−	0.126193i
$494$	50661.5	+	60852.9i	0.207598	+	0.249360i
$495$	−171767.	−	263752.i	−0.701018	−	1.07643i
$496$	−38059.6	+	99734.9i	−0.154704	+	0.405400i
$497$	126562.	+	126562.i	0.512378	+	0.512378i
$498$	7002.40	−	150912.i	0.0282350	−	0.608507i
$499$	−418419.			−1.68039			−0.840196	−	0.542283i	$-0.817560\pi$
$499$	−418419.			−1.68039			−0.840196	+	0.542283i	$0.817560\pi$
$500$	−71475.9	+	239565.i	−0.285904	+	0.958258i
$501$	−27581.2	+	1235.65i	−0.109885	+	0.00492290i
$502$	59761.7	+	5461.68i	0.237146	+	0.0216730i
$503$	117529.	+	117529.i	0.464524	+	0.464524i	0.900135	−	0.435611i	$-0.143468\pi$
$503$	117529.	+	117529.i	0.464524	+	0.464524i	−0.435611	+	0.900135i	$0.643468\pi$
$504$	−240254.	+	164905.i	−0.945822	+	0.649193i
$505$	−28116.1	−	53004.6i	−0.110249	−	0.207841i
$506$	−177115.	−	212745.i	−0.691758	−	0.830917i
$507$	−12476.6	+	13646.9i	−0.0485378	+	0.0530908i
$508$	205644.	+	298584.i	0.796872	+	1.15702i
$509$	−209943.			−0.810337			−0.405169	−	0.914242i	$-0.632787\pi$
$509$	−209943.			−0.810337			−0.405169	+	0.914242i	$0.632787\pi$
$510$	−82124.2	−	173838.i	−0.315741	−	0.668349i
$511$		−	534075.i		−	2.04532i
$512$	−178794.	−	191708.i	−0.682045	−	0.731310i
$513$	−53718.3	+	70503.9i	−0.204121	+	0.267904i
$514$	−27006.6	−	32439.4i	−0.102222	−	0.122785i
$515$	104936.	−	342026.i	0.395650	−	1.28957i
$516$	−41469.4	−	5738.47i	−0.155750	−	0.0215525i
$517$	−370819.	+	370819.i	−1.38733	+	1.38733i
$518$	−327415.	−	29922.8i	−1.22022	−	0.111517i
$519$	65790.8	−	2947.47i	0.244248	−	0.0109424i
$520$	219154.	+	140812.i	0.810481	+	0.520756i
$521$		−	109507.i		−	0.403430i	−0.979444	−	0.201715i	$-0.935349\pi$
$521$		−	109507.i		−	0.403430i	0.979444	−	0.201715i	$-0.0646515\pi$
$522$	−105.031	+	65787.1i	−0.000385456	+	0.241435i
$523$	11086.8	−	11086.8i	0.0405326	−	0.0405326i	−0.686550	−	0.727083i	$-0.740876\pi$
$523$	11086.8	−	11086.8i	0.0405326	−	0.0405326i	0.727083	+	0.686550i	$0.240876\pi$
$524$	77299.0	+	14247.9i	0.281521	+	0.0518905i
$525$	269461.	+	165434.i	0.977636	+	0.600215i
$526$	60081.2	+	72167.5i	0.217154	+	0.260838i
$527$	−62988.3	+	62988.3i	−0.226798	+	0.226798i
$528$	−160786.	−	319995.i	−0.576741	−	1.14782i
$529$		−	81601.2i		−	0.291599i
$530$	180782.	−	441270.i	0.643581	−	1.57091i
$531$	83510.3	−	7497.67i	0.296177	−	0.0265912i
$532$	62027.5	+	90060.6i	0.219160	+	0.318208i
$533$	−312980.	+	312980.i	−1.10170	+	1.10170i
$534$	246542.	+	270535.i	0.864586	+	0.948725i
$535$	−46848.1	+	152695.i	−0.163676	+	0.533480i
$536$	−195656.	−	348162.i	−0.681025	−	1.21186i
$537$	185383.	−	202772.i	0.642866	−	0.703169i
$538$	75515.0	+	6901.40i	0.260897	+	0.0238436i
$539$			117941.i			0.405965i
$540$	−98797.7	+	274353.i	−0.338812	+	0.940854i
$541$	238352.			0.814376			0.407188	−	0.913344i	$-0.366509\pi$
$541$	238352.			0.814376			0.407188	+	0.913344i	$0.366509\pi$
$542$	15789.2	−	172766.i	0.0537481	−	0.588111i
$543$	80382.1	+	73488.6i	0.272621	+	0.249242i
$544$	−70823.9	−	206967.i	−0.239322	−	0.699363i
$545$	69042.4	+	130159.i	0.232447	+	0.438209i
$546$	243514.	−	221918.i	0.816843	−	0.744400i
$547$	390656.	+	390656.i	1.30563	+	1.30563i	0.924536	+	0.381094i	$0.124453\pi$
$547$	390656.	+	390656.i	1.30563	+	1.30563i	0.381094	+	0.924536i	$0.375547\pi$
$548$	99071.0	+	143846.i	0.329902	+	0.479001i
$549$	35210.8	+	392184.i	0.116824	+	1.30120i
$550$	−246303.	+	300553.i	−0.814225	+	0.993562i
$551$	24687.8			0.0813166
$552$	−58127.9	+	249785.i	−0.190769	+	0.819761i
$553$	171649.	+	171649.i	0.561294	+	0.561294i
$554$	30709.8	−	25566.7i	0.100059	−	0.0833018i
$555$	−283452.	+	167024.i	−0.920223	+	0.542242i
$556$	84896.3	+	15648.2i	0.274624	+	0.0506192i
$557$	139994.	+	139994.i	0.451230	+	0.451230i	0.895763	−	0.444533i	$-0.146630\pi$
$557$	139994.	+	139994.i	0.451230	+	0.451230i	−0.444533	+	0.895763i	$0.646630\pi$
$558$	135105.	+	215.699i	0.433915	+	0.000692755i
$559$	47332.6			0.151474
$560$	283710.	+	221210.i	0.904687	+	0.705388i
$561$	−13374.6	−	298537.i	−0.0424968	−	0.948576i
$562$	55186.2	−	603848.i	0.174726	−	1.91185i
$563$	17283.4	+	17283.4i	0.0545270	+	0.0545270i	0.733845	−	0.679317i	$-0.237724\pi$
$563$	17283.4	+	17283.4i	0.0545270	+	0.0545270i	−0.679317	+	0.733845i	$0.737724\pi$
$564$	481256.	+	66595.4i	1.51293	+	0.209356i
$565$	80424.5	−	262133.i	0.251937	−	0.821155i
$566$	30767.7	−	25614.8i	0.0960421	−	0.0799573i
$567$	303068.	+	210162.i	0.942702	+	0.653716i
$568$	196214.	+	55025.6i	0.608182	+	0.170556i
$569$	276293.			0.853387			0.426694	−	0.904396i	$-0.359678\pi$
$569$	276293.			0.853387			0.426694	+	0.904396i	$0.359678\pi$
$570$	103015.	+	36911.1i	0.317066	+	0.113608i
$571$		−	327932.i		−	1.00580i	−0.864344	−	0.502901i	$-0.832266\pi$
$571$		−	327932.i		−	1.00580i	0.864344	−	0.502901i	$-0.167734\pi$
$572$	229662.	+	333457.i	0.701936	+	1.01917i
$573$	328896.	+	300690.i	1.00173	+	0.915819i
$574$	−469790.	+	391111.i	−1.42587	+	1.18707i
$575$	273267.	−	52559.5i	0.826517	−	0.158970i
$576$	−146484.	+	297687.i	−0.441514	+	0.897254i
$577$	−49652.9	+	49652.9i	−0.149140	+	0.149140i	−0.777734	−	0.628594i	$-0.783631\pi$
$577$	−49652.9	+	49652.9i	−0.149140	+	0.149140i	0.628594	+	0.777734i	$0.283631\pi$
$578$	−13792.5	+	150917.i	−0.0412844	+	0.451734i
$579$	11992.9	+	267695.i	0.0357739	+	0.798515i
$580$	77459.7	−	24422.9i	0.230261	−	0.0726008i
$581$			235895.i			0.698821i
$582$	−98924.4	−	4590.14i	−0.292050	−	0.0135513i
$583$	524114.	−	524114.i	1.54201	−	1.54201i
$584$	−297898.	−	530099.i	−0.873459	−	1.55429i
$585$	68129.5	−	322570.i	0.199078	−	0.942568i
$586$	−106017.	+	88261.5i	−0.308730	+	0.257025i
$587$	−47552.9	+	47552.9i	−0.138007	+	0.138007i	−0.772735	−	0.634728i	$-0.781112\pi$
$587$	−47552.9	+	47552.9i	−0.138007	+	0.138007i	0.634728	+	0.772735i	$0.281112\pi$
$588$	87124.0	−	65942.8i	0.251990	−	0.190727i
$589$		−	50700.7i		−	0.146145i
$590$	−39982.9	−	95480.2i	−0.114860	−	0.274290i
$591$	768.942	+	17163.7i	0.00220150	+	0.0491400i
$592$	−341668.	+	152927.i	−0.974901	+	0.436354i
$593$	323567.	−	323567.i	0.920141	−	0.920141i	−0.0768982	−	0.997039i	$-0.524502\pi$
$593$	323567.	−	323567.i	0.920141	−	0.920141i	0.997039	+	0.0768982i	$0.0245016\pi$
$594$	−306360.	+	334026.i	−0.868280	+	0.946688i
$595$	140676.	+	265203.i	0.397362	+	0.749107i
$596$	−3911.18	−	720.915i	−0.0110107	−	0.00202951i
$597$	−115841.	−	105907.i	−0.325023	−	0.297149i
$598$	26389.4	−	288752.i	0.0737949	−	0.807464i
$599$		−	375636.i		−	1.04692i	−0.852050	−	0.523461i	$-0.824641\pi$
$599$		−	375636.i		−	1.04692i	0.852050	−	0.523461i	$-0.175359\pi$
$600$	359731.	+	13901.9i	0.999254	+	0.0386163i
$601$	241686.			0.669118			0.334559	−	0.942375i	$-0.391413\pi$
$601$	241686.			0.669118			0.334559	+	0.942375i	$0.391413\pi$
$602$	65098.0	+	5949.37i	0.179628	+	0.0164164i
$603$	−324019.	+	387939.i	−0.891119	+	1.06691i
$604$	22024.0	−	119487.i	0.0603701	−	0.327526i
$605$	−210219.	+	111510.i	−0.574329	+	0.304651i
$606$	−63860.2	+	58196.7i	−0.173894	+	0.158472i
$607$	−351226.	−	351226.i	−0.953256	−	0.953256i	0.0456993	−	0.998955i	$-0.485448\pi$
$607$	−351226.	−	351226.i	−0.953256	−	0.953256i	−0.998955	+	0.0456993i	$0.985448\pi$
$608$	111800.	+	54792.2i	0.302437	+	0.148222i
$609$	−4597.44	−	102620.i	−0.0123960	−	0.276693i
$610$	448397.	−	187769.i	1.20504	−	0.504619i
$611$	−549299.			−1.47138
$612$	−213053.	+	176796.i	−0.568832	+	0.472031i
$613$	−270470.	−	270470.i	−0.719777	−	0.719777i	0.248782	−	0.968559i	$-0.419970\pi$
$613$	−270470.	−	270470.i	−0.719777	−	0.719777i	−0.968559	+	0.248782i	$0.919970\pi$
$614$	−38872.0	−	46691.7i	−0.103110	−	0.123852i
$615$	−153067.	+	592238.i	−0.404697	+	1.56584i
$616$	273948.	+	487480.i	0.721949	+	1.28468i
$617$	−342842.	−	342842.i	−0.900584	−	0.900584i	0.0949028	−	0.995487i	$-0.469746\pi$
$617$	−342842.	−	342842.i	−0.900584	−	0.900584i	−0.995487	+	0.0949028i	$0.969746\pi$
$618$	−514623.	−	23878.7i	−1.34745	−	0.0625222i
$619$	−462673.			−1.20751			−0.603757	−	0.797168i	$-0.706330\pi$
$619$	−462673.			−1.20751			−0.603757	+	0.797168i	$0.706330\pi$
$620$	−50156.7	−	159077.i	−0.130481	−	0.413832i
$621$	321658.	−	43464.1i	0.834086	−	0.112706i
$622$	−602576.	−	55070.0i	−1.55751	−	0.142342i
$623$	−404128.	−	404128.i	−1.04122	−	1.04122i
$624$	117919.	−	356093.i	0.302841	−	0.914523i
$625$	−144903.	−	362755.i	−0.370952	−	0.928652i
$626$	378354.	+	454466.i	0.965494	+	1.15972i
$627$	125532.	+	114767.i	0.319316	+	0.291932i
$628$	−362205.	+	249462.i	−0.918407	+	0.632535i
$629$	−312365.			−0.789515
$630$	134245.	−	435077.i	0.338235	−	1.09619i
$631$			76183.3i			0.191338i	0.995413	+	0.0956689i	$0.0304990\pi$
$631$			76183.3i			0.191338i	−0.995413	+	0.0956689i	$0.969501\pi$
$632$	266114.	+	74628.0i	0.666244	+	0.186839i
$633$	−434713.	+	475490.i	−1.08491	+	1.18668i
$634$	299603.	+	359873.i	0.745362	+	0.895304i
$635$	−541567.	−	166157.i	−1.34309	−	0.412070i
$636$	−680205.	−	94125.6i	−1.68161	−	0.232698i
$637$	−87354.1	+	87354.1i	−0.215280	+	0.215280i
$638$	125717.	+	11489.4i	0.308854	+	0.0282265i
$639$	−23063.1	−	256880.i	−0.0564827	−	0.629114i
$640$	404985.	+	61314.0i	0.988733	+	0.149692i
$641$		−	126882.i		−	0.308805i	−0.988008	−	0.154402i	$-0.950655\pi$
$641$		−	126882.i		−	0.308805i	0.988008	−	0.154402i	$-0.0493452\pi$
$642$	229750.	+	10660.5i	0.557424	+	0.0258647i
$643$	236786.	−	236786.i	0.572710	−	0.572710i	−0.360175	−	0.932885i	$-0.617283\pi$
$643$	236786.	−	236786.i	0.572710	−	0.572710i	0.932885	+	0.360175i	$0.117283\pi$
$644$	72588.1	−	393813.i	0.175023	−	0.949550i
$645$	56357.1	−	33208.4i	0.135466	−	0.0798232i
$646$	66473.4	+	79845.7i	0.159288	+	0.191332i
$647$	16460.6	−	16460.6i	0.0393222	−	0.0393222i	−0.687172	−	0.726494i	$-0.741148\pi$
$647$	16460.6	−	16460.6i	0.0393222	−	0.0393222i	0.726494	+	0.687172i	$0.241148\pi$
$648$	418037.	+	39551.2i	0.995554	+	0.0941910i
$649$		−	160895.i		−	0.381991i
$650$	−405032.	+	40180.3i	−0.958656	+	0.0951012i
$651$	−210749.	+	9441.66i	−0.497282	+	0.0222785i
$652$	546521.	−	376406.i	1.28562	−	0.885445i
$653$	364090.	−	364090.i	0.853852	−	0.853852i	−0.136753	−	0.990605i	$-0.543667\pi$
$653$	364090.	−	364090.i	0.853852	−	0.853852i	0.990605	+	0.136753i	$0.0436667\pi$
$654$	156816.	−	142909.i	0.366636	−	0.334120i
$655$	−108495.	+	57551.0i	−0.252888	+	0.134144i
$656$	−248137.	+	650240.i	−0.576612	+	1.51101i
$657$	−493339.	+	590662.i	−1.14292	+	1.36839i
$658$	−755467.	−	69042.9i	−1.74487	−	0.159466i
$659$			510689.i			1.17594i	0.808882	+	0.587971i	$0.200073\pi$
$659$			510689.i			1.17594i	−0.808882	+	0.587971i	$0.799927\pi$
$660$	507402.	+	235904.i	1.16483	+	0.541560i
$661$	−488763.			−1.11865			−0.559327	−	0.828947i	$-0.688940\pi$
$661$	−488763.			−1.11865			−0.559327	+	0.828947i	$0.688940\pi$
$662$	28742.8	−	314504.i	0.0655863	−	0.717645i
$663$	211207.	−	231019.i	0.480487	−	0.525558i
$664$	131578.	+	234139.i	0.298434	+	0.531052i
$665$	−163350.	−	50117.2i	−0.369383	−	0.113330i
$666$	334465.	+	335535.i	0.754054	+	0.756465i
$667$	−63925.9	−	63925.9i	−0.143690	−	0.143690i
$668$	40422.7	−	27840.3i	0.0905883	−	0.0623909i
$669$	678441.	−	30394.6i	1.51586	−	0.0679116i
$670$	577438.	+	236568.i	1.28634	+	0.526996i
$671$	755600.			1.67821
$672$	206936.	−	474925.i	0.458244	−	1.05169i
$673$	−253733.	−	253733.i	−0.560204	−	0.560204i	0.369161	−	0.929365i	$-0.379645\pi$
$673$	−253733.	−	253733.i	−0.560204	−	0.560204i	−0.929365	+	0.369161i	$0.879645\pi$
$674$	−338819.	+	282075.i	−0.745844	+	0.620933i
$675$	−145195.	−	431871.i	−0.318673	−	0.947865i
$676$	5958.69	−	32327.7i	0.0130394	−	0.0707427i
$677$	−593769.	−	593769.i	−1.29551	−	1.29551i	−0.931329	−	0.364180i	$-0.881349\pi$
$677$	−593769.	−	593769.i	−1.29551	−	1.29551i	−0.364180	−	0.931329i	$-0.618651\pi$
$678$	−394414.	−	18301.0i	−0.858011	−	0.0398121i
$679$	154631.			0.335396
$680$	287554.	+	184761.i	0.621873	+	0.399571i
$681$	338529.	−	15166.3i	0.729964	−	0.0327028i
$682$	23595.5	−	258182.i	0.0507296	−	0.555083i
$683$	25575.3	+	25575.3i	0.0548251	+	0.0548251i	0.733988	−	0.679163i	$-0.237657\pi$
$683$	25575.3	+	25575.3i	0.0548251	+	0.0548251i	−0.679163	+	0.733988i	$0.737657\pi$
$684$	14591.8	−	156899.i	0.0311887	−	0.335358i
$685$	−260905.	−	80047.7i	−0.556034	−	0.170596i
$686$	283777.	−	236251.i	0.603016	−	0.502025i
$687$	−247847.	+	271096.i	−0.525134	+	0.574393i
$688$	67931.8	−	30405.5i	0.143515	−	0.0642355i
$689$	776376.			1.63544
$690$	−171167.	−	362320.i	−0.359519	−	0.761017i
$691$			485021.i			1.01579i	0.861418	+	0.507896i	$0.169577\pi$
$691$			485021.i			1.01579i	−0.861418	+	0.507896i	$0.830423\pi$
$692$	−96422.4	+	66409.1i	−0.201357	+	0.138680i
$693$	453676.	−	543175.i	0.944668	−	1.13103i
$694$	−98053.8	+	81632.1i	−0.203585	+	0.169489i
$695$	−119159.	+	63207.3i	−0.246692	+	0.130857i
$696$	−61803.0	−	99291.8i	−0.127583	−	0.204972i
$697$	−410664.	+	410664.i	−0.845320	+	0.845320i
$698$	68554.2	−	750120.i	0.140709	−	1.53964i
$699$	−526460.	+	23585.7i	−1.07749	+	0.0482720i
$700$	−562103.	+	4351.51i	−1.14715	+	0.00888062i
$701$		−	110924.i		−	0.225731i	−0.993610	−	0.112865i	$-0.963997\pi$
$701$		−	110924.i		−	0.225731i	0.993610	−	0.112865i	$-0.0360029\pi$
$702$	−474306.	+	20490.5i	−0.962464	+	0.0415794i
$703$	125715.	−	125715.i	0.254376	−	0.254376i
$704$	543817.	+	331048.i	1.09726	+	0.667952i
$705$	−654028.	+	385387.i	−1.31589	+	0.775387i
$706$	−520459.	+	433295.i	−1.04418	+	0.869309i
$707$	95395.1	−	95395.1i	0.190848	−	0.190848i
$708$	−118854.	+	89958.8i	−0.237108	+	0.179464i
$709$			30332.5i			0.0603414i	0.999545	+	0.0301707i	$0.00960509\pi$
$709$			30332.5i			0.0603414i	−0.999545	+	0.0301707i	$0.990395\pi$
$710$	−293700.	+	122989.i	−0.582623	+	0.243977i
$711$	−31279.1	−	348392.i	−0.0618750	−	0.689174i
$712$	−626535.	−	175703.i	−1.23591	−	0.346593i
$713$	−131283.	+	131283.i	−0.258244	+	0.258244i
$714$	319517.	−	291180.i	0.626755	−	0.571171i
$715$	−604819.	−	185563.i	−1.18308	−	0.362978i
$716$	−88536.8	+	480339.i	−0.172702	+	0.936962i
$717$	87282.8	−	95470.3i	0.169782	−	0.185708i
$718$	11663.4	−	127621.i	0.0226244	−	0.247556i
$719$			759919.i			1.46997i	0.678082	+	0.734986i	$0.262811\pi$
$719$			759919.i			1.46997i	−0.678082	+	0.734986i	$0.737189\pi$
$720$	−109433.	−	506718.i	−0.211097	−	0.977465i
$721$	804421.			1.54744
$722$	460233.	+	42061.1i	0.882883	+	0.0806876i
$723$	52092.7	+	47625.3i	0.0996553	+	0.0911090i
$724$	−190414.	−	35097.4i	−0.363264	−	0.0669573i
$725$	−71171.0	+	105068.i	−0.135403	+	0.199892i
$726$	230811.	+	253273.i	0.437908	+	0.480524i
$727$	608555.	+	608555.i	1.15141	+	1.15141i	0.986270	+	0.165143i	$0.0528087\pi$
$727$	608555.	+	608555.i	1.15141	+	1.15141i	0.165143	+	0.986270i	$0.447191\pi$
$728$	−158154.	+	563957.i	−0.298413	+	1.06410i
$729$	−141047.	−	512382.i	−0.265405	−	0.964137i
$730$	879186.	+	360190.i	1.64982	+	0.675906i
$731$	62105.6			0.116224
$732$	−422467.	−	558166.i	−0.788444	−	1.04170i
$733$	344086.	+	344086.i	0.640411	+	0.640411i	0.950656	−	0.310246i	$-0.100411\pi$
$733$	344086.	+	344086.i	0.640411	+	0.640411i	−0.310246	+	0.950656i	$0.600411\pi$
$734$	488228.	+	586443.i	0.906213	+	1.08851i
$735$	−42721.6	+	165296.i	−0.0790812	+	0.305977i
$736$	−147614.	−	431369.i	−0.272504	−	0.796331i
$737$	685847.	+	685847.i	1.26268	+	1.26268i
$738$	880845.	+	1406.29i	1.61729	+	0.00258203i
$739$	761771.			1.39488			0.697438	−	0.716645i	$-0.254323\pi$
$739$	761771.			1.39488			0.697438	+	0.716645i	$0.254323\pi$
$740$	270073.	−	518805.i	0.493194	−	0.947416i
$741$	7973.57	+	177979.i	0.0145217	+	0.324140i
$742$	1.06777e6	+	97584.9i	1.93942	+	0.177245i
$743$	−354077.	−	354077.i	−0.641387	−	0.641387i	0.309509	−	0.950896i	$-0.399835\pi$
$743$	−354077.	−	354077.i	−0.641387	−	0.641387i	−0.950896	+	0.309509i	$0.899835\pi$
$744$	−203913.	+	126923.i	−0.368383	+	0.229296i
$745$	5489.66	−	2911.97i	0.00989083	−	0.00524656i
$746$	−192465.	−	231182.i	−0.345838	−	0.415410i
$747$	217902.	−	260889.i	0.390499	−	0.467535i
$748$	301342.	+	437533.i	0.538588	+	0.782001i
$749$	−359128.			−0.640156
$750$	−454065.	+	332011.i	−0.807227	+	0.590241i
$751$		−	605917.i		−	1.07432i	−0.843481	−	0.537159i	$-0.819497\pi$
$751$		−	605917.i		−	1.07432i	0.843481	−	0.537159i	$-0.180503\pi$
$752$	−788354.	+	352858.i	−1.39407	+	0.623971i
$753$	99653.9	+	91107.7i	0.175754	+	0.160681i
$754$	84603.5	+	101623.i	0.148815	+	0.178751i
$755$	88960.7	+	167709.i	0.156065	+	0.294213i
$756$	−654903.	−	31435.7i	−1.14586	−	0.0550021i
$757$	624388.	−	624388.i	1.08959	−	1.08959i	0.0940193	−	0.995570i	$-0.470028\pi$
$757$	624388.	−	624388.i	1.08959	−	1.08959i	0.995570	−	0.0940193i	$-0.0299716\pi$
$758$	451604.	+	41272.6i	0.785995	+	0.0718329i
$759$	−27876.0	−	622224.i	−0.0483890	−	1.08010i
$760$	−190089.	+	41370.1i	−0.329101	+	0.0716242i
$761$			1.01368e6i			1.75038i	0.483781	+	0.875189i	$0.339263\pi$
$761$			1.01368e6i			1.75038i	−0.483781	+	0.875189i	$0.660737\pi$
$762$	−37809.8	+	814859.i	−0.0651170	+	1.40337i
$763$	−234254.	+	234254.i	−0.402381	+	0.402381i
$764$	−779108.	−	143606.i	−1.33478	−	0.246029i
$765$	89393.5	−	423248.i	0.152751	−	0.723222i
$766$	−161137.	−	193552.i	−0.274623	−	0.329868i
$767$	119168.	−	119168.i	0.202567	−	0.202567i
$768$	−59509.8	−	586814.i	−0.100894	−	0.994897i
$769$			589476.i			0.996812i	0.866944	+	0.498406i	$0.166081\pi$
$769$			589476.i			0.996812i	−0.866944	+	0.498406i	$0.833919\pi$
$770$	−808502.	−	331232.i	−1.36364	−	0.558664i
$771$	−4250.55	−	94877.0i	−0.00715049	−	0.159607i
$772$	−270210.	−	392331.i	−0.453385	−	0.658291i
$773$	−254771.	+	254771.i	−0.426375	+	0.426375i	−0.887392	−	0.461017i	$-0.847485\pi$
$773$	−254771.	+	254771.i	−0.426375	+	0.426375i	0.461017	+	0.887392i	$0.347485\pi$
$774$	−66499.8	−	66712.4i	−0.111004	−	0.111359i
$775$	215777.	+	146162.i	0.359254	+	0.243350i
$776$	153480.	−	86250.8i	0.254876	−	0.143232i
$777$	−545971.	−	499149.i	−0.904332	−	0.826777i
$778$	−322426.	−	29466.9i	−0.532686	−	0.0486827i
$779$		−	330553.i		−	0.544711i
$780$	201087.	+	550534.i	0.330518	+	0.904889i
$781$	−494918.			−0.811394
$782$	34625.8	−	378875.i	0.0566221	−	0.619558i
$783$	−89708.4	+	117740.i	−0.146322	+	0.192044i
$784$	−69256.2	+	181485.i	−0.112675	+	0.295263i
$785$	201561.	−	656962.i	0.327090	−	1.06611i
$786$	119123.	+	130716.i	0.192819	+	0.211584i
$787$	237434.	+	237434.i	0.383349	+	0.383349i	0.872307	−	0.488958i	$-0.162623\pi$
$787$	237434.	+	237434.i	0.383349	+	0.383349i	−0.488958	+	0.872307i	$0.662623\pi$
$788$	−17324.9	−	25154.9i	−0.0279010	−	0.0405107i
$789$	9456.13	+	211072.i	0.0151901	+	0.339059i
$790$	−398329.	+	166802.i	−0.638245	+	0.267269i
$791$	616518.			0.985355
$792$	147325.	−	792184.i	0.234869	−	1.26292i
$793$	559640.	+	559640.i	0.889943	+	0.889943i
$794$	−343686.	+	286127.i	−0.545156	+	0.453855i
$795$	924400.	−	544704.i	1.46260	−	0.861839i
$796$	274411.	+	50579.9i	0.433088	+	0.0798274i
$797$	−40477.4	−	40477.4i	−0.0637229	−	0.0637229i	0.674527	−	0.738250i	$-0.264348\pi$
$797$	−40477.4	−	40477.4i	−0.0637229	−	0.0637229i	−0.738250	+	0.674527i	$0.764348\pi$
$798$	−11404.4	+	245782.i	−0.0179088	+	0.385962i
$799$	−720741.			−1.12898
$800$	−555491.	+	317851.i	−0.867955	+	0.496642i
$801$	73643.2	+	820250.i	0.114780	+	1.27844i
$802$	5959.79	−	65212.0i	0.00926578	−	0.101386i
$803$	1.04424e6	+	1.04424e6i	1.61946	+	1.61946i
$804$	123171.	−	890106.i	0.190545	−	1.37699i
$805$	293203.	+	552747.i	0.452457	+	0.852972i
$806$	208701.	−	173748.i	0.321258	−	0.267455i
$807$	125923.	+	115124.i	0.193356	+	0.176774i
$808$	41475.1	−	147895.i	0.0635279	−	0.226532i
$809$	62323.1			0.0952253			0.0476126	−	0.998866i	$-0.484839\pi$
$809$	62323.1			0.0952253			0.0476126	+	0.998866i	$0.484839\pi$
$810$	−550361.	+	357169.i	−0.838837	+	0.544382i
$811$		−	593343.i		−	0.902120i	−0.892494	−	0.451060i	$-0.851046\pi$
$811$		−	593343.i		−	0.902120i	0.892494	−	0.451060i	$-0.148954\pi$
$812$	103584.	+	150399.i	0.157102	+	0.228104i
$813$	263384.	−	288091.i	0.398482	−	0.435861i
$814$	698680.	−	581668.i	1.05446	−	0.877862i
$815$	−304130.	+	991272.i	−0.457872	+	1.49237i
$816$	154723.	−	467234.i	0.232367	−	0.701704i
$817$	−24995.1	+	24995.1i	−0.0374465	+	0.0374465i
$818$	91066.2	−	996446.i	0.136098	−	1.48918i
$819$	738324.	−	66287.7i	1.10073	−	0.0988247i
$820$	−327006.	−	1.03713e6i	−0.486327	−	1.54243i
$821$			310064.i			0.460007i	0.973190	+	0.230003i	$0.0738738\pi$
$821$			310064.i			0.460007i	−0.973190	+	0.230003i	$0.926126\pi$
$822$	−18215.2	+	392566.i	−0.0269582	+	0.580991i
$823$	−551920.	+	551920.i	−0.814847	+	0.814847i	−0.985356	−	0.170509i	$-0.945459\pi$
$823$	−551920.	+	551920.i	−0.814847	+	0.814847i	0.170509	+	0.985356i	$0.445459\pi$
$824$	798432.	−	448693.i	1.17594	−	0.660837i
$825$	−850325.	+	203397.i	−1.24933	+	0.298839i
$826$	178874.	−	148917.i	0.262172	−	0.218265i
$827$	131499.	−	131499.i	0.192270	−	0.192270i	−0.604407	−	0.796676i	$-0.706590\pi$
$827$	131499.	−	131499.i	0.192270	−	0.192270i	0.796676	+	0.604407i	$0.206590\pi$
$828$	−444054.	+	368487.i	−0.647702	+	0.537479i
$829$		−	290146.i		−	0.422189i	−0.977466	−	0.211094i	$-0.932297\pi$
$829$		−	290146.i		−	0.422189i	0.977466	−	0.211094i	$-0.0677028\pi$
$830$	−388326.	−	159092.i	−0.563691	−	0.230936i
$831$	89818.4	−	4023.92i	0.130066	−	0.00582703i
$832$	157589.	+	647974.i	0.227656	+	0.936076i
$833$	−114618.	+	114618.i	−0.165182	+	0.165182i
$834$	130831.	+	143563.i	0.188095	+	0.206400i
$835$	−22494.5	+	73318.0i	−0.0322629	+	0.105157i
$836$	−297369.	−	54811.4i	−0.425483	−	0.0784257i
$837$	241800.	+	184232.i	0.345148	+	0.262975i
$838$	15400.9	−	168517.i	0.0219310	−	0.239969i
$839$		−	793352.i		−	1.12705i	−0.826100	−	0.563523i	$-0.809446\pi$
$839$		−	793352.i		−	1.12705i	0.826100	−	0.563523i	$-0.190554\pi$
$840$	207363.	+	782442.i	0.293882	+	1.10890i
$841$	−666053.			−0.941709
$842$	−786818.	−	71908.1i	−1.10981	−	0.101427i
$843$	920576.	−	1.00693e6i	1.29540	−	1.41692i
$844$	207614.	−	1.12637e6i	0.291455	−	1.58123i
$845$	24068.8	+	45374.5i	0.0337086	+	0.0635475i
$846$	771735.	+	774203.i	1.07827	+	1.08172i
$847$	−378341.	−	378341.i	−0.527372	−	0.527372i
$848$	1.11426e6	−	498728.i	1.54951	−	0.693541i
$849$	89987.6	−	4031.50i	0.124844	−	0.00559308i
$850$	−531447.	+	52721.0i	−0.735567	+	0.0729702i
$851$	−651044.			−0.898983
$852$	276716.	+	365599.i	0.381202	+	0.503646i
$853$	155621.	+	155621.i	0.213880	+	0.213880i	0.805914	−	0.592033i	$-0.201675\pi$
$853$	155621.	+	155621.i	0.213880	+	0.213880i	−0.592033	+	0.805914i	$0.701675\pi$
$854$	699347.	+	840032.i	0.958908	+	1.15181i
$855$	134363.	+	206318.i	0.183801	+	0.282232i
$856$	−356454.	+	200316.i	−0.486470	+	0.273380i
$857$	866383.	+	866383.i	1.17964	+	1.17964i	0.979837	+	0.199800i	$0.0640293\pi$
$857$	866383.	+	866383.i	1.17964	+	1.17964i	0.199800	+	0.979837i	$0.435971\pi$
$858$	−42225.8	+	910030.i	−0.0573592	+	1.23618i
$859$	−791139.			−1.07218			−0.536088	−	0.844162i	$-0.680099\pi$
$859$	−791139.			−1.07218			−0.536088	+	0.844162i	$0.680099\pi$
$860$	−53697.1	+	103151.i	−0.0726029	+	0.139469i
$861$	−1.37401e6	+	61556.7i	−1.85347	+	0.0830364i
$862$	954726.	+	87253.4i	1.28489	+	0.117427i
$863$	−372787.	−	372787.i	−0.500540	−	0.500540i	0.411065	−	0.911606i	$-0.365157\pi$
$863$	−372787.	−	372787.i	−0.500540	−	0.500540i	−0.911606	+	0.411065i	$0.865157\pi$
$864$	−667562.	+	334092.i	−0.894260	+	0.447548i
$865$	53657.4	−	174889.i	0.0717129	−	0.233739i
$866$	−8142.44	−	9780.43i	−0.0108572	−	0.0130413i
$867$	−230076.	+	251658.i	−0.306078	+	0.334790i
$868$	308871.	−	212729.i	0.409957	−	0.282350i
$869$	−671229.			−0.888855
$870$	172032.	+	61640.7i	0.227285	+	0.0814384i
$871$			1.01595e6i			1.33918i
$872$	−101847.	+	363172.i	−0.133941	+	0.477617i
$873$	−171015.	−	142837.i	−0.224391	−	0.187418i
$874$	138547.	+	166418.i	0.181374	+	0.217860i
$875$	684207.	−	550722.i	0.893658	−	0.719310i
$876$	187536.	−	1.35524e6i	0.244386	−	1.76607i
$877$	97315.8	−	97315.8i	0.126527	−	0.126527i	−0.641007	−	0.767535i	$-0.721483\pi$
$877$	97315.8	−	97315.8i	0.126527	−	0.126527i	0.767535	+	0.641007i	$0.221483\pi$
$878$	−1.04263e6	−	95286.7i	−1.35251	−	0.123607i
$879$	−310072.	+	13891.4i	−0.401314	+	0.0179791i
$880$	−987239.	+	122203.i	−1.27484	+	0.157804i
$881$		−	1.20777e6i		−	1.55609i	−0.628212	−	0.778043i	$-0.716213\pi$
$881$		−	1.20777e6i		−	1.55609i	0.628212	−	0.778043i	$-0.283787\pi$
$882$	245848.	+	392.502i	0.316031	+	0.000504551i
$883$	−481027.	+	481027.i	−0.616948	+	0.616948i	−0.944747	−	0.327799i	$-0.893693\pi$
$883$	−481027.	+	481027.i	−0.616948	+	0.616948i	0.327799	+	0.944747i	$0.393693\pi$
$884$	−100870.	+	547252.i	−0.129080	+	0.700298i
$885$	58280.6	−	225496.i	0.0744110	−	0.287907i
$886$	−714061.	−	857706.i	−0.909636	−	1.09262i
$887$	−902512.	+	902512.i	−1.14711	+	1.14711i	−0.159993	+	0.987118i	$0.551147\pi$
$887$	−902512.	+	902512.i	−1.14711	+	1.14711i	−0.987118	+	0.159993i	$0.948853\pi$
$888$	−820324.	−	190899.i	−1.04030	−	0.242091i
$889$		−	1.27373e6i		−	1.61166i
$890$	937820.	−	392718.i	1.18397	−	0.495793i
$891$	−1.00349e6	+	181654.i	−1.26403	+	0.228817i
$892$	−994317.	+	684817.i	−1.24967	+	0.860686i
$893$	290070.	−	290070.i	0.363748	−	0.363748i
$894$	−6027.40	−	6613.96i	−0.00754145	−	0.00827535i
$895$	−357624.	−	674194.i	−0.446458	−	0.841664i
$896$	135291.	+	910986.i	0.168521	+	1.13474i
$897$	440208.	−	481501.i	0.547108	−	0.598428i
$898$	−1856.01	−	169.622i	−0.00230159	−	0.000210344i
$899$		−	84669.1i		−	0.104762i
$900$	625680.	+	514417.i	0.772444	+	0.635083i
$901$	1.01869e6			1.25485
$902$	153835.	−	1.68327e6i	0.189079	−	2.06890i
$903$	108552.	+	99243.0i	0.133126	+	0.121709i
$904$	611928.	−	343884.i	0.748796	−	0.420799i
$905$	267261.	−	141768.i	0.326316	−	0.173094i
$906$	202056.	−	184137.i	0.246159	−	0.224328i
$907$	−236675.	−	236675.i	−0.287698	−	0.287698i	0.548471	−	0.836169i	$-0.315210\pi$
$907$	−236675.	−	236675.i	−0.287698	−	0.287698i	−0.836169	+	0.548471i	$0.815210\pi$
$908$	−496144.	+	341710.i	−0.601778	+	0.414463i
$909$	−193621.	+	17383.6i	−0.234329	+	0.0210384i
$910$	−353493.	−	844152.i	−0.426873	−	1.01938i
$911$	1.00644e6			1.21269			0.606346	−	0.795201i	$-0.292635\pi$
$911$	1.00644e6			1.21269			0.606346	+	0.795201i	$0.292635\pi$
$912$	125774.	+	250314.i	0.151217	+	0.300950i
$913$	−461231.	−	461231.i	−0.553320	−	0.553320i
$914$	−495951.	+	412891.i	−0.593671	+	0.494245i
$915$	1.05898e6	+	273699.i	1.26487	+	0.326912i
$916$	118369.	−	642188.i	0.141074	−	0.765370i
$917$	−195264.	−	195264.i	−0.232212	−	0.232212i
$918$	−622342.	+	26885.8i	−0.738489	+	0.0319034i
$919$	1.34582e6			1.59352			0.796758	−	0.604298i	$-0.206546\pi$
$919$	1.34582e6			1.59352			0.796758	+	0.604298i	$0.206546\pi$
$920$	599334.	+	385088.i	0.708097	+	0.454972i
$921$	−6118.03	−	136561.i	−0.00721261	−	0.160994i
$922$	11204.1	−	122595.i	0.0131799	−	0.144215i
$923$	−366565.	−	366565.i	−0.430276	−	0.430276i
$924$	−172459.	+	1.24628e6i	−0.201995	+	1.45973i
$925$	172612.	+	897444.i	0.201738	+	1.04887i
$926$	−448108.	+	373061.i	−0.522590	+	0.435069i
$927$	−889652.	−	743064.i	−1.03529	−	0.864703i
$928$	186703.	+	91501.7i	0.216799	+	0.106251i
$929$	−1.01547e6			−1.17661			−0.588307	−	0.808637i	$-0.700205\pi$
$929$	−1.01547e6			−1.17661			−0.588307	+	0.808637i	$0.700205\pi$
$930$	126590.	−	353299.i	0.146364	−	0.408485i
$931$		−	92258.9i		−	0.106441i
$932$	771575.	−	531407.i	0.888273	−	0.611781i
$933$	−1.00481e6	−	918638.i	−1.15430	−	1.05531i
$934$	−806456.	+	671394.i	−0.924458	+	0.769633i
$935$	−793590.	−	243479.i	−0.907764	−	0.278509i
$936$	695853.	−	477619.i	0.794266	−	0.545168i
$937$	−262877.	+	262877.i	−0.299415	+	0.299415i	−0.840785	−	0.541370i	$-0.817906\pi$
$937$	−262877.	+	262877.i	−0.299415	+	0.299415i	0.541370	+	0.840785i	$0.317906\pi$
$938$	−127698.	+	1.39727e6i	−0.145137	+	1.58809i
$939$	59548.8	+	1.32920e6i	0.0675371	+	1.50750i
$940$	623159.	−	1.19708e6i	0.705250	−	1.35477i
$941$		−	1.20288e6i		−	1.35845i	−0.733931	−	0.679224i	$-0.762316\pi$
$941$		−	1.20288e6i		−	1.35845i	0.733931	−	0.679224i	$-0.237684\pi$
$942$	−988485.	−	45866.1i	−1.11396	−	0.0516881i
$943$	−855924.	+	855924.i	−0.962525	+	0.962525i
$944$	94478.8	−	247581.i	0.106021	−	0.277826i
$945$	832585.	−	596932.i	0.932320	−	0.668439i
$946$	−138915.	+	115650.i	−0.155226	+	0.129230i
$947$	837336.	−	837336.i	0.933684	−	0.933684i	−0.0642501	−	0.997934i	$-0.520466\pi$
$947$	837336.	−	837336.i	0.933684	−	0.933684i	0.997934	+	0.0642501i	$0.0204655\pi$
$948$	375294.	+	495840.i	0.417595	+	0.551728i
$949$			1.54685e6i			1.71758i
$950$	192669.	−	235105.i	0.213483	−	0.260504i
$951$	47154.3	+	1.05254e6i	0.0521387	+	1.16379i
$952$	−207516.	+	739974.i	−0.228969	+	0.816474i
$953$	−459396.	+	459396.i	−0.505826	+	0.505826i	−0.913242	−	0.407417i	$-0.866430\pi$
$953$	−459396.	+	459396.i	−0.505826	+	0.505826i	0.407417	+	0.913242i	$0.366430\pi$
$954$	−1.09077e6	−	1.09425e6i	−1.19849	−	1.20232i
$955$	1.09354e6	−	580065.i	1.19902	−	0.636019i
$956$	−41685.4	+	226156.i	−0.0456108	+	0.247453i
$957$	209636.	+	191658.i	0.228898	+	0.209268i
$958$	−59151.2	+	647232.i	−0.0644514	+	0.705227i
$959$		−	613630.i		−	0.667220i
$960$	642252.	+	660953.i	0.696888	+	0.717180i
$961$	749638.			0.811717
$962$	948299.	+	86666.0i	1.02470	+	0.0936480i
$963$	397179.	+	331736.i	0.428286	+	0.357717i
$964$	−123400.	−	22745.4i	−0.132789	−	0.0244759i
$965$	711604.	+	218326.i	0.764159	+	0.234450i
$966$	665952.	−	606892.i	0.713656	−	0.650365i
$967$	70699.2	+	70699.2i	0.0756069	+	0.0756069i	0.743899	−	0.668292i	$-0.232974\pi$
$967$	70699.2	+	70699.2i	0.0756069	+	0.0756069i	−0.668292	+	0.743899i	$0.732974\pi$
$968$	−586557.	−	164492.i	−0.625979	−	0.175547i
$969$	10462.2	+	233528.i	0.0111423	+	0.248709i
$970$	−104286.	+	254552.i	−0.110837	+	0.270541i
$971$	−1.67722e6			−1.77890			−0.889452	−	0.457028i	$-0.848914\pi$
$971$	−1.67722e6			−1.77890			−0.889452	+	0.457028i	$0.848914\pi$
$972$	695254.	+	639717.i	0.735887	+	0.677104i
$973$	−214456.	−	214456.i	−0.226523	−	0.226523i
$974$	−381452.	−	458188.i	−0.402089	−	0.482976i
$975$	−780446.	−	479151.i	−0.820982	−	0.504038i
$976$	1.16270e6	+	443694.i	1.22058	+	0.465784i
$977$	−536099.	−	536099.i	−0.561637	−	0.561637i	0.368135	−	0.929772i	$-0.379996\pi$
$977$	−536099.	−	536099.i	−0.561637	−	0.561637i	−0.929772	+	0.368135i	$0.879996\pi$
$978$	1.49150e6	+	69206.2i	1.55936	+	0.0723548i
$979$	1.58033e6			1.64886
$980$	−91269.0	−	289469.i	−0.0950322	−	0.301404i
$981$	475460.	−	42687.4i	0.494055	−	0.0443570i
$982$	−214735.	−	19624.9i	−0.222679	−	0.0203509i
$983$	−606321.	−	606321.i	−0.627474	−	0.627474i	0.319958	−	0.947432i	$-0.396331\pi$
$983$	−606321.	−	606321.i	−0.627474	−	0.627474i	−0.947432	+	0.319958i	$0.896331\pi$
$984$	−1.32945e6	+	827501.i	−1.37304	+	0.854630i
$985$	45625.5	+	13998.3i	0.0470257	+	0.0144279i
$986$	111009.	+	133340.i	0.114184	+	0.137154i
$987$	−1.25976e6	−	1.15172e6i	−1.29316	−	1.18226i
$988$	−179652.	−	260844.i	−0.184042	−	0.267219i
$989$	129443.			0.132339
$990$	588198.	+	1.11316e6i	0.600141	+	1.13576i
$991$			1.37314e6i			1.39820i	0.715025	+	0.699099i	$0.246415\pi$
$991$			1.37314e6i			1.39820i	−0.715025	+	0.699099i	$0.753585\pi$
$992$	187915.	−	383428.i	0.190958	−	0.389638i
$993$	479466.	−	524442.i	0.486250	−	0.531862i
$994$	−458073.	−	550222.i	−0.463620	−	0.556884i
$995$	−385158.	+	204306.i	−0.389039	+	0.206365i
$996$	−82832.5	+	598595.i	−0.0834991	+	0.603412i
$997$	523631.	−	523631.i	0.526787	−	0.526787i	−0.392826	−	0.919613i	$-0.628502\pi$
$997$	523631.	−	523631.i	0.526787	−	0.526787i	0.919613	+	0.392826i	$0.128502\pi$
$998$	1.66673e6	+	152324.i	1.67342	+	0.152935i
$999$	142742.	+	1.05636e6i	0.143028	+	1.05848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.l.a.23.2	✓	88
3.2	odd	2	inner	60.5.l.a.23.43	yes	88
4.3	odd	2	inner	60.5.l.a.23.21	yes	88
5.2	odd	4	inner	60.5.l.a.47.24	yes	88
12.11	even	2	inner	60.5.l.a.23.24	yes	88
15.2	even	4	inner	60.5.l.a.47.21	yes	88
20.7	even	4	inner	60.5.l.a.47.43	yes	88
60.47	odd	4	inner	60.5.l.a.47.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.l.a.23.2	✓	88	1.1	even	1	trivial
60.5.l.a.23.21	yes	88	4.3	odd	2	inner
60.5.l.a.23.24	yes	88	12.11	even	2	inner
60.5.l.a.23.43	yes	88	3.2	odd	2	inner
60.5.l.a.47.2	yes	88	60.47	odd	4	inner
60.5.l.a.47.21	yes	88	15.2	even	4	inner
60.5.l.a.47.24	yes	88	5.2	odd	4	inner
60.5.l.a.47.43	yes	88	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.98340 - 0.364047i) q^{2} +(-6.64241 - 6.07276i) q^{3} +(15.7349 + 2.90029i) q^{4} +(-22.0852 + 11.7150i) q^{5} +(24.2486 + 26.6084i) q^{6} +(-39.7479 - 39.7479i) q^{7} +(-61.6227 - 17.2813i) q^{8} +(7.24316 + 80.6755i) q^{9} +O(q^{10})\)	\(q+(-3.98340 - 0.364047i) q^{2} +(-6.64241 - 6.07276i) q^{3} +(15.7349 + 2.90029i) q^{4} +(-22.0852 + 11.7150i) q^{5} +(24.2486 + 26.6084i) q^{6} +(-39.7479 - 39.7479i) q^{7} +(-61.6227 - 17.2813i) q^{8} +(7.24316 + 80.6755i) q^{9} +(92.2391 - 38.6257i) q^{10} +155.433 q^{11} +(-86.9051 - 114.819i) q^{12} +(115.123 + 115.123i) q^{13} +(143.862 + 172.802i) q^{14} +(217.842 + 56.3022i) q^{15} +(239.177 + 91.2717i) q^{16} +(151.054 + 151.054i) q^{17} +(0.517273 - 324.000i) q^{18} -121.587 q^{19} +(-381.487 + 120.282i) q^{20} +(22.6423 + 505.401i) q^{21} +(-619.153 - 56.5850i) q^{22} +(314.833 + 314.833i) q^{23} +(304.378 + 489.009i) q^{24} +(350.515 - 517.459i) q^{25} +(-416.670 - 500.490i) q^{26} +(441.811 - 579.866i) q^{27} +(-510.150 - 740.711i) q^{28} -203.047 q^{29} +(-847.254 - 303.579i) q^{30} +416.993i q^{31} +(-919.509 - 450.643i) q^{32} +(-1032.45 - 943.909i) q^{33} +(-546.717 - 656.698i) q^{34} +(1343.49 + 412.193i) q^{35} +(-120.012 + 1290.43i) q^{36} +(-1033.95 + 1033.95i) q^{37} +(484.328 + 44.2632i) q^{38} +(-65.5793 - 1463.80i) q^{39} +(1563.40 - 340.252i) q^{40} +2718.66i q^{41} +(93.7965 - 2021.46i) q^{42} +(205.575 - 205.575i) q^{43} +(2445.73 + 450.801i) q^{44} +(-1105.08 - 1696.88i) q^{45} +(-1139.49 - 1368.72i) q^{46} +(-2385.71 + 2385.71i) q^{47} +(-1034.44 - 2058.73i) q^{48} +758.791i q^{49} +(-1584.62 + 1933.64i) q^{50} +(-86.0473 - 1920.67i) q^{51} +(1477.56 + 2145.34i) q^{52} +(3371.95 - 3371.95i) q^{53} +(-1971.01 + 2149.00i) q^{54} +(-3432.78 + 1820.91i) q^{55} +(1762.48 + 3136.27i) q^{56} +(807.628 + 738.367i) q^{57} +(808.817 + 73.9186i) q^{58} -1035.14i q^{59} +(3264.44 + 1517.72i) q^{60} +4861.25 q^{61} +(151.805 - 1661.05i) q^{62} +(2918.78 - 3494.58i) q^{63} +(3498.72 + 2129.84i) q^{64} +(-3891.18 - 1193.84i) q^{65} +(3769.04 + 4135.83i) q^{66} +(4412.48 + 4412.48i) q^{67} +(1938.72 + 2814.92i) q^{68} +(-179.344 - 4003.16i) q^{69} +(-5201.60 - 2131.02i) q^{70} -3184.12 q^{71} +(947.831 - 5096.61i) q^{72} +(6718.28 + 6718.28i) q^{73} +(4495.05 - 3742.24i) q^{74} +(-5470.67 + 1308.58i) q^{75} +(-1913.16 - 352.636i) q^{76} +(-6178.15 - 6178.15i) q^{77} +(-271.665 + 5854.79i) q^{78} -4318.43 q^{79} +(-6351.53 + 786.209i) q^{80} +(-6456.07 + 1168.69i) q^{81} +(989.720 - 10829.5i) q^{82} +(-2967.39 - 2967.39i) q^{83} +(-1109.53 + 8018.13i) q^{84} +(-5105.66 - 1566.46i) q^{85} +(-893.725 + 744.047i) q^{86} +(1348.72 + 1233.06i) q^{87} +(-9578.22 - 2686.08i) q^{88} +10167.3 q^{89} +(3784.25 + 7161.67i) q^{90} -9151.77i q^{91} +(4040.77 + 5866.99i) q^{92} +(2532.30 - 2769.83i) q^{93} +(10371.7 - 8634.73i) q^{94} +(2685.27 - 1424.39i) q^{95} +(3371.10 + 8577.31i) q^{96} +(-1945.15 + 1945.15i) q^{97} +(276.236 - 3022.57i) q^{98} +(1125.83 + 12539.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^6	\( 88 q - 4 q^{6} + 148 q^{10} - 164 q^{12} - 8 q^{13} - 484 q^{16} + 456 q^{18} + 600 q^{21} - 348 q^{22} - 8 q^{25} - 148 q^{28} + 68 q^{30} - 328 q^{33} - 1556 q^{36} + 2232 q^{37} + 2024 q^{40} - 2116 q^{42} - 2504 q^{45} - 4432 q^{46} + 1540 q^{48} + 80 q^{52} + 3192 q^{57} - 1948 q^{58} + 2836 q^{60} - 7568 q^{61} + 3384 q^{66} + 8348 q^{70} + 5256 q^{72} + 5592 q^{73} - 256 q^{76} + 13176 q^{78} - 12648 q^{81} + 20400 q^{82} + 5816 q^{85} + 7932 q^{88} - 13152 q^{90} + 3680 q^{93} - 18028 q^{96} - 15208 q^{97}+O(q^{100}) \) 88 * q - 4 * q^6 + 148 * q^10 - 164 * q^12 - 8 * q^13 - 484 * q^16 + 456 * q^18 + 600 * q^21 - 348 * q^22 - 8 * q^25 - 148 * q^28 + 68 * q^30 - 328 * q^33 - 1556 * q^36 + 2232 * q^37 + 2024 * q^40 - 2116 * q^42 - 2504 * q^45 - 4432 * q^46 + 1540 * q^48 + 80 * q^52 + 3192 * q^57 - 1948 * q^58 + 2836 * q^60 - 7568 * q^61 + 3384 * q^66 + 8348 * q^70 + 5256 * q^72 + 5592 * q^73 - 256 * q^76 + 13176 * q^78 - 12648 * q^81 + 20400 * q^82 + 5816 * q^85 + 7932 * q^88 - 13152 * q^90 + 3680 * q^93 - 18028 * q^96 - 15208 * q^97

Introduction

L-functions

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